Why does my Unit Test work from Visual Studio 2010 and not with Jenkins?
As I've noted in the comment, you can create a slave instance (even on the same machine) that would run as a regular user in the foreground. Tie the jobs that would not run in the service instance to that slave.
Double-check that the user account Jenkins is running under is able to interact with the desktop.
Ie, run services.msc, select your Jenkins service, bring up properties, switch to 'Log On' tab and verify that the 'Allow service to interact with desktop' box is checked.
Generally you'll want to do this if there's any kind of a dialog that pops up when something in your test runs (even if it doesn't require input of any kind).