Supposing you are working in Windows, before launching CVI you must configure your port in control panel, indicating 'no handshaking' as the last parameter in system/ports/comx/port settings.
Once in CVI, opening the serial port this way
OpenComConfig (com, "", 19200, 0, 8, 1, 512, 512);
should work well for connecting your two computers.
This example is for 19200 baud rate, no parity, 8 data bit, 1 stop bit and tx/rx buffers that usually are enough but that can be set to the value more suitable for your application. To communicate with ordinary acquisition devices I usually leave the default values. You can adjust parameters as your actual configuration needs, maintaining the same settings on both PCs.
The "" tells the serial driver to use standard Windows name
s instead of writing a specific names. This can prevent conflicts in naming ports and is usually the best thing to do.
Nothing else is necessary.
You could even try the communication by means of function panels for ComWrt and ComRd: if in HyperTerminal communication works, it means that there are not mistakes in cabling and after a ComWrt in one station the other should read the entire message sent by ComRd.
Sorry for generic response: if you add more details to your message we will help you better.
Roberto