As it is an instrument I presume you want to send a SCPI command and then read the response within a short time.
For SerialPort.ReadLine to work, the response must contain a termination character equal to the one set by the property SerialPort.NewLine (default is Line Feed).
So read the documentation and check what termination character the instrument is using.
Or it could be that the instrument is expecting as specific termination character to process a command.
Same thing, read the communication.
If the instrument accepts the command sent, you can also check by sending a command that is visibly detectable on the instrument, such as turning off the display or something similar.
When dealing with serial port communication, there is a nice tool called PortMon.
PortMon will monitor everything that is happening on the serial port and is very useful in this kind of situations.
It is a free tool and you can download it here:
Portmon for Windows[
^]
Using PortMon you can compare what data is sent when you are using HyperTerminal (and it works) with your own application (and it doesn't work).