It could well be the case that your app is dependent on a component that is up to date on XP systems but Win2K either lacks or has an older version of. One likely candidate is MDAC if your app uses OleDb. If that's the case then try downloading the latest version of MDAC from Microsoft and installing it on the Win2K system. If that doesn't work then you would need to consider what other components your app is dependent on.

Also, did you simply copy your executable to the target system or did you use an installer?