Convert any base biginteger to base 10 and convert back base again

Your code is a mess of cascading conversions, you need to check that every conversion works as expected, use the debugger to do so.
BigValue and TenBase are BigInteger, and you want
TenBase = ToTenBase(BigValue, 3)
see what you do with ToTenBase
ToTenBase does BigValue as BigInteger => ToString => ToCharArray => ToString => ToBigInteger => ToString => ToBigInteger
advice: you have BigInteger, you want BigInteger, stay BigInteger.
-----
There is a rather simple way to extract digits from a number without convertion to string
BI = 22222222210222211011111222011100022001111
Un = BI % 10 = 1
Tn = BI / 10 = 2222222221022221101111122201110002200111
repeat operation for each digit you need.
-----
There is a tool that allow you to see what your code is doing, its name is debugger. It is also a great learning tool because it show you reality and you can see which expectation match reality.
When you don't understand what your code is doing or why it does what it does, the answer is debugger.
Use the debugger to see what your code is doing. Just set a breakpoint and see your code performing, the debugger allow you to execute lines 1 by 1 and to inspect variables as it execute.

Debugger - Wikipedia, the free encyclopedia[^]
Visual Basic / Visual Studio Video Tutorial - Basic Debugging - YouTube[^]
Visual Basic .NET programming for Beginners - Breakpoints and Debugging Tools[^]
The debugger is here to show you what your code is doing and your task is to compare with what it should do.
There is no magic in the debugger, it don't find bugs, it just help you to. When the code don't do what is expected, you are close to a bug.

Have you heard of Horner's method[^]? It can remove the need to take the power of numbers, and you generally don't want to do that, since it is very slow.

The call and check code is:

string input = "22222222210222211011111222011100022001111";
string Base = "012";
BigInteger base10number = ToBase10Horner(input, Base);
var output = FromBase10(base10number, Base);
var IsTheSameNumber = input.Equals(output.ToString());

What I did was the following code:

static string FromBase10(BigInteger value, string BaseChars)
{
    int sign = 1;
    if (value < 0)
    {
        sign = -1;
    }
    else if (value == 0)
    {
        return BaseChars.ToCharArray()[0].ToString();
    }
    value *= sign;

    StringBuilder Result = new StringBuilder();
    int nBase = BaseChars.Length;
    BigInteger Reminder = value;

    do
    {
        BigInteger ModnBase = (Reminder % nBase);
        Result.Append(BaseChars.ToCharArray()[(int)ModnBase]);
        Reminder /= nBase;
    } while (Reminder != 0);
    if (sign == -1)
        Result.Append('-');

    char[] charArray = Result.ToString().ToCharArray();
    Array.Reverse(charArray);
    return new string(charArray);
}

static BigInteger ToBase10Horner(string Value, string BaseChars)
{
    BigInteger nBase = BaseChars.Length;
    int count = Value.Length - 1;
    BigInteger nResult = 0;

    for (int i = 0; i < count; i++)
    {
        nResult = nBase * (nResult + (BigInteger)BaseChars.ToUpper().IndexOf(Value.ToCharArray()[i]));
    }

    nResult += (BigInteger)BaseChars.ToUpper().IndexOf(Value.ToCharArray()[count]);

    return (nResult);
}

I found this solution and working now. Thanks to Kornfeld Eliyahu Peter for contributions. ( On-What-Base-Do-You-Stand)

 Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
     Dim BigValue As BigInteger = BigInteger.Parse("22222222210222211011111222011100022001111")
     Dim TenBase As BigInteger = ToTenBase(BigValue, 3)
     Dim TenBaseByte As Byte() = BigValue.ToByteArray
     Dim TreeBase As BigInteger = FromTenBase(TenBase, 3)
     If BigValue.ToString <> TreeBase.ToString Then Stop
 End Sub

Function ToTenBase(ByVal BigValue As BigInteger, ByVal Base As Integer) As BigInteger
     Dim Total As BigInteger
     Dim str As String = BigValue.ToString
     str = StrReverse(str)
     For i As Integer = str.Length - 1 To 0 Step -1
         Dim k As Integer = Microsoft.VisualBasic.Val(str(i))
         Total = Total + k * (Base) ^ i
     Next
     Return Total
 End Function

 Function FromTenBase(BigValue As BigInteger, Base As Integer) As BigInteger
     Dim BigByte() As Byte = BigValue.ToByteArray
     Dim Remaining As Numerics.BigInteger = BigValue
     Dim Count As Integer = Fix(Math.Log(BigValue, Base))
     Dim Result(Count) As Byte
     Do Until Remaining <= 0
         Dim Pow As Integer = Fix(Math.Log(Remaining, Base))
         Dim Division As BigInteger = Remaining / Base ^ Pow
         Result(Pow) = Division
         Remaining = Remaining - (Division* Base ^ Pow)
     Loop
     Array.Reverse(Result)
     Return BigInteger.Parse(ArrayToString(Result))
 End Function

 Function ArrayToString(ByVal Arr As Array) As String
     Dim s As String
     For i As Integer = 0 To Arr.Length - 1
         s = s & Arr(i)
     Next
     Return s
 End Function

Converted Kenneth Haugland's solution to vb.net for vb.net users.

Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
    Dim input As String = "222222222102222110111112220111000220011110000011112222101111222011"
    Dim Base As String = "012"
    Dim base10number As BigInteger = ToBase10Horner(input, Base)
    Dim output = FromBase10(base10number, Base)
    Dim IsTheSameNumber = input.Equals(output.ToString())
End Sub

Private Shared Function FromBase10(value As BigInteger, BaseChars As String) As String
    Dim sign As Integer = 1
    If value < 0 Then
        sign = -1
    ElseIf value = 0 Then
        Return BaseChars.ToCharArray()(0).ToString()
    End If
    value *= sign

    Dim Result As New StringBuilder()
    Dim nBase As Integer = BaseChars.Length
    Dim Reminder As BigInteger = value

    Do
        Dim ModnBase As BigInteger = (Reminder Mod nBase)
        Result.Append(BaseChars.ToCharArray()(ModnBase))
        Reminder /= nBase
    Loop While Reminder <> 0
    If sign = -1 Then
        Result.Append("-"c)
    End If

    Dim charArray As Char() = Result.ToString().ToCharArray()
    Array.Reverse(charArray)
    Return New String(charArray)
End Function

Private Shared Function ToBase10Horner(Value As String, BaseChars As String) As BigInteger
    Dim nBase As BigInteger = BaseChars.Length
    Dim count As Integer = Value.Length - 1
    Dim nResult As BigInteger = 0

    Dim i As Integer = 0
    While i < count
        Dim bi As BigInteger = BaseChars.ToUpper().IndexOf(Value.ToCharArray()(i))
        nResult = nBase * (nResult + bi)
        System.Math.Max(System.Threading.Interlocked.Increment(i), i - 1)
    End While
    Dim co As BigInteger = BaseChars.ToUpper().IndexOf(Value.ToCharArray()(count))
    nResult += co

    Return (nResult)
End Function