Can anybody point me to an application that would monitor a PC (or program) and as it is running show what drives (especially network drives) are being accessed?
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Monitor Network Drive Access
You may have the answer already on your machine. Right click on My Computer -> Manage -> Performance Logs and Alerts -> Trace logs
Teach yourself how to create a trace Log for Disk I/O and File I/O, start and stop the trace log, etc. Process the log with the commandline tool "tracerpt.exe". like most all Windows programs, use the /? switch to learn the commandline options. You'll get a .csv file you can open with Excel or OO and then do custom filters to find the info you want.
How do I know all this? Because I just taught myself all that in the last 20 minutes so you should have no problem figure it all out.
Tracerpt.exe may or may not be in a Windows Resource Kit or Support Tool download. I'll leave that for you to figure out too.