C#

        /* http://msdn.microsoft.com/en-us/library/ms893424.aspx
  VOID FAR PASCAL lineCallbackFunc( 
  DWORD hDevice, 
  DWORD dwMsg, 
  DWORD dwCallbackInstance, 
  DWORD dwParam1, 
  DWORD dwParam2, 
  DWORD dwParam3
);*/
        private delegate void lineCallbackFunc(
            uint hDevice,
            uint dwMsg,
            uint dwCallbackInstance,
            uint dwParam1,
            uint dwParam2,
            uint dwParam3);

        /* http://msdn.microsoft.com/en-us/library/ms894378.aspx
typedef struct lineinitializeexparams_tag {
  DWORD dwTotalSize;
  DWORD dwNeededSize;
  DWORD dwUsedSize;
  DWORD dwOptions;
  union {
    HANDLE hEvent;
    HANDLE hCompletionPort;
  } Handles;
  DWORD dwCompletionKey;
} LINEINITIALIZEEXPARAMS, FAR* LPLINEINITIALIZEEXPARAMS;*/

        [StructLayout(LayoutKind.Sequential)]
        private struct LINEINITIALIZEEXPARAMS
        {
            public uint dwTotalSize;
            public uint dwNeededSize;
            public uint dwUsedSize;
            public uint dwOptions;
            public IntPtr hEvent;
            public IntPtr hCompletionPort;
            public uint dwCompletionKey;
        }


        /* http://msdn.microsoft.com/en-us/library/ms894370.aspx
  LONG WINAPI lineInitializeEx(
  LPHLINEAPP lphLineApp,
  HINSTANCE hInstance,
  LINECALLBACK lpfnCallback,
  LPCWSTR lpszFriendlyAppName,
  LPDWORD lpdwNumDevs,
  LPDWORD lpdwAPIVersion,
  LPLINEINITIALIZEEXPARAMS lpLineInitializeExParams
);*/
        [DllImport("cellcore.dll", SetLastError = true)]
        private static extern uint lineInitializeEx(
            out IntPtr lphLineApp, // edit: this is a pointer to a handle so added 'out'
            IntPtr hInstance,
            lineCallbackFunc lpfnCallback,
            StringBuilder lpszFriendlyAppName,
            out uint lpdwNumDevs,
            out uint lpdwAPIVersion,
            ref LINEINITIALIZEEXPARAMS lpLineInitializeExParams
            );

[StructLayout(LayoutKind.Explict)]
private struct LINEINITIALIZEEXPARAMS
{
    [FieldOffset(0)]
    public uint dwTotalSize;
    [FieldOffset(4)]
    public uint dwNeededSize;
    [FieldOffset(8)]
    public uint dwUsedSize;
    [FieldOffset(12)]
    public IntPtr hEvent;
    public IntPtr hCompletionPort;
    [FieldOffset(12)]
    public uint dwCompletionKey;
}

DaveyM69 wrote:

[FieldOffset(12)]
public uint dwCompletionKey;

typedef struct lineinitializeexparams_tag {
  DWORD dwTotalSize;
  DWORD dwNeededSize;
  DWORD dwUsedSize;
  DWORD dwOptions;
  union {
    HANDLE hEvent;
    HANDLE hCompletionPort;
  } Handles;
  DWORD dwCompletionKey;
} LINEINITIALIZEEXPARAMS, *LPLINEINITIALIZEEXPARAMS;

/* http://msdn.microsoft.com/en-us/library/dd757347(v=VS.85).aspx
       typedef struct mmtime_tag {
           UINT wType;
           union {
               DWORD  ms;
               DWORD  sample;
               DWORD  cb;
               DWORD  ticks;
               struct {
                   BYTE hour;
                   BYTE min;
                   BYTE sec;
                   BYTE frame;
                   BYTE fps;
                   BYTE dummy;
                   BYTE pad[2];
               } smpte;
               struct {
                   DWORD songptrpos;
               } midi;
           } u;
       } MMTIME, *PMMTIME, *LPMMTIME; */
    /// <summary>
    /// Contains timing information for different types of multimedia data.
    /// </summary>
    [StructLayout(LayoutKind.Explicit)]
    internal struct MMTIME
    {
        /// <summary>
        /// Time format.
        /// </summary>
        [FieldOffset(0)]
        public uint wType;
        /// <summary>
        /// Number of milliseconds.
        /// Used when wType is TIME_MS.
        /// </summary>
        [FieldOffset(4)]
        public uint ms;
        /// <summary>
        /// Number of samples.
        /// Used when wType is TIME_SAMPLES.
        /// </summary>
        [FieldOffset(4)]
        public uint sample;
        /// <summary>
        /// Byte count.
        /// Used when wType is TIME_BYTES.
        /// </summary>
        [FieldOffset(4)]
        public uint cb;
        /// <summary>
        /// Ticks in MIDI stream.
        /// Used when wType is TIME_TICKS.
        /// </summary>
        [FieldOffset(4)]
        public uint ticks;
        /// <summary>
        /// Hours.
        /// Used when wType is TIME_SMPTE.
        /// </summary>
        [FieldOffset(4)]
        public byte hour;
        /// <summary>
        /// Minutes.
        /// Used when wType is TIME_SMPTE.
        /// </summary>
        [FieldOffset(5)]
        public byte min;
        /// <summary>
        /// Seconds.
        /// Used when wType is TIME_SMPTE.
        /// </summary>
        [FieldOffset(6)]
        public byte sec;
        /// <summary>
        /// Frames.
        /// Used when wType is TIME_SMPTE.
        /// </summary>
        [FieldOffset(7)]
        public byte frame;
        /// <summary>
        /// Frames per second (24, 25, 29 (30 drop), or 30).
        /// Used when wType is TIME_SMPTE.
        /// </summary>
        [FieldOffset(8)]
        public byte fps;
        /// <summary>
        /// Dummy byte for alignment.
        /// Used when wType is TIME_SMPTE.
        /// </summary>
        [FieldOffset(9)]
        private byte dummy;
        /// <summary>
        /// Padding.
        /// Used when wType is TIME_SMPTE.
        /// </summary>
        [FieldOffset(10)]
        private ushort pad;
        /// <summary>
        /// Song pointer position.
        /// Used when wType is TIME_MIDI.
        /// </summary>
        [FieldOffset(4)]
        public uint songptrpos;
    }

Luc Pattyn wrote:

there seems to be a dwOptions member too, which hasn't been mentioned before!

[StructLayout(LayoutKind.Sequential)]
private struct LINEINITIALIZEEXPARAMS
{
    public uint dwTotalSize;
    public uint dwNeededSize;
    public uint dwUsedSize;
    public uint dwOptions;
    public IntPtr handle; // Will be either hEvent OR hCompletionPort
    public uint dwCompletionKey;
}

IntPtr hInstance = System.Diagnostics.Process.GetCurrentProcess().Handle;

/// <summary>
/// No error.
/// </summary>
public const uint LINEERR_NOERROR = 0x00000000;
/// <summary>
/// Invalid application name.
/// </summary>
public const uint LINEERR_INVALAPPNAME = 0x80000015;
/// <summary>
/// The INI file is corrupted.
/// </summary>
public const uint LINEERR_INIFILECORRUPT = 0x8000000E;
/// <summary>
/// Invalid parameter.
/// </summary>
public const uint LINEERR_INVALPARAM = 0x80000032;
/// <summary>
/// Invalid pointer.
/// </summary>
public const uint LINEERR_INVALPOINTER = 0x80000035;
/// <summary>
/// No memory available.
/// </summary>
public const uint LINEERR_NOMEM = 0x80000044;
/// <summary>
/// The operation failed.
/// </summary>
public const uint LINEERR_OPERATIONFAILED = 0x80000048;
/// <summary>
/// The application attempted to initialize TAPI twice.
/// </summary>
public const uint LINEERR_REINIT = 0x80000052;

public bool OpenLine()
{
    UInt32 dwDevNum = 0;//count the devices
    UInt32 dwApiVerSion = TAPI_CURRENT_VERSION;
    LINEINITIALIZEEXPARAMS dtParams = new LINEINITIALIZEEXPARAMS();
    dtParams.dwTotalSize = (UInt32)Marshal.SizeOf(dtParams);
    dtParams.dwOptions = 1;
    IntPtr handles = new IntPtr(0);

    IntPtr hInstance = IntPtr.Zero;//new IntPtr(GetModuleHandle(new IntPtr(0)).ToInt32());
    unsafe
    {
        fixed(IntPtr *hLineApp = &m_hLineApp)
        {
            long lResult = lineInitializeEx(hLineApp, hInstance, new IntPtr(0), new IntPtr(0),
                new IntPtr(&dwDevNum), new IntPtr(&dwApiVerSion), new IntPtr(&dtParams));
            if (lResult == 0)
            {
                return true;
            }
        }
        return false;
    }
}
[StructLayout(LayoutKind.Sequential)]
private struct LINEINITIALIZEEXPARAMS
{
    public uint dwTotalSize;
    public uint dwNeededSize;
    public uint dwUsedSize;
    public uint dwOptions;
    public IntPtr hMultiUse;
    public uint dwCompletionKey;
}
[DllImport("coredll.dll", SetLastError = true)]
unsafe private static extern uint lineInitializeEx(
    IntPtr *lphLineApp,
    IntPtr hInstance,
    IntPtr pfnCallback,//lineCallbackFunc lpfnCallback,
    IntPtr FriendAppName,//StringBuilder lpszFriendlyAppName,
    IntPtr pNumDevs,//out uint lpdwNumDevs,
    IntPtr pAPIVersion,//out uint lpdwAPIVersion,
    IntPtr pLineInitializeExParams);//ref LINEINITIALIZEEXPARAMS lpLineInitializeExParams);