TSR?!? That stands for "Terminate and Stay Resident", and is a concept which (rightfully) vanished when we got rid of DOS. Programs under Windows (post-Windows 9x, at least) do not TSR.
Task Manager will show you every process running under Windows. It's not particularly user-friendly, because it refers to programs by filename, which may not be how you know them. Still, it's part of Windows, so it's not a bad place to start. If you press Ctrl+Alt+Del the dialog that appears has a button to start Task Manager.
The big question for the OP is what are you really asking? When you say "How do I find a program that is still running in the background", what are you trying to find? There are several ways to interpret this question, and you may get mightily confused if we explain the answer to the wrong question