With RS-232, you have to send a query to receive data. You might not see it, but that's what the manufacturer's software does. The same is true from Hyperterminal or LabVIEW. Now, I'm not used to HyperTerminal so I don't know why it bugs you, but with LabVIEW, make sure you check these things:
To which COM port is your DMM connected?
What is the command (query) to fetch data? (the manual is 55MB and takes forever to download, so I don't think I'll have the patience to finish the download)
Have you installed VISA drivers from NI? You should get an error message like this if you didn't:
Error -1073807202 occurred at Property Node (arg 1) in VISA Configure Serial Port (Instr).vi->Basic Serial Write and Read.vi Possible reason(s): LabVIEW: (Hex 0xBFFF009E) VISA or a code library required by VISA could not be located or loaded. This is usually due to a required driver not being installed on the system.
Using the "Basic Serial Write and Read.vi" example you got from NI examples is exactly where you should start. To query the DMM, you've got to have both "write" and "read" switches to ON position. In the "string to write", put the query command. Then press the start Arrow and you should get the data in "read string". Make sure you have the right COM port selected in "VISA resource name".