Some wild guesses:

Aside from looking at Task Manager, you could try renaming the EXE file. If the program is running you won't be able to rename it. Granted, this assumes that user has appropriate access rights to the folder and its contents to perform the rename.

Another thing you could check -- the shorcut they're using to start the program. Had one case where we were getting all sorts of errors when use was trying to start the program. Turned out he simply copied the EXE file to his desktop rather than creating a shortcut, so the program couldn't find necessary files to run properly.

Ran into a head-scratcher once before involving XP Mode under Win7 (with a similar sort of thing happening under remote desktop as well). If you've got a configuration where program gets launched in remote session with only the application window showing on terminal desktop (i.e. it looks like the program is on your desktop, though it is actually running elsewhere), you could get into puzzling situation where program might appear to freeze when a window from another application pops up in front. In the situation I was running into, there was a warning dialog (from the antivirus) popped up over the application and grabbed focus (basically it was system modal) -- but since the viewport was limited only to the application window, the warning popup wasn't visible and I couldn't regain focus. It wasn't until I'd launched the remote session with the full desktop did I see what was going on (I was able to see the system modal dialog).