Serial port problems are usually pretty straightforward to solve.
Check that you have a proper serial port cable, not a null modem cable (the receive and transmit lines are crossed in the cable) between the PC and the device.
If you are on a Windows XP system, use HyperTerm (Start->Accessories->Communications->HyperTerm) otherwise, download TeraTerm (it's free - search on TeraTerm).
Set up HyperTerm to use the proper COM port, and configure the baud rate, stop bits, etc. for your device.
Send a command string for the device and check the response.
If everything works, great. If not, start playing with baud rates and other parameters.
Once you are communicating successfully via HyperTerm, then move to LabVIEW to open and configure the port, then send and receive characters
Good Luck.