Install a clean machine to test deploy on, you're really shooting in the dark if you aren't. If you don't have another machine, install a virtual machine. Not all virtual machine solutions have drivers that support the graphics device XNA needs - but some do. And with a virtual machine you can install a trial version of Windows and make use of snapshots to revert to a clean slate every time you do new tests.
Provide useful error reports, catch crashes and display them to the end-user with an option to send and/or copy information to you. If it does automatic updates, you might want them to opt-in for automatic error and crash reports so you get a database of common problems complete with stack traces that you might want to fix. The only case where this won't work as far as I know is if .NET isn't installed on the target machine.
There's a multitude of possible issues from content pipelines not handling decimal point differences in other cultures beside the one they were compiled with to installations missing a vital file or directx and c++ dependencies. It's hard or impossible to answer your question until you've figured out why it's crashing and what the demo thinks is missing (if anything).