My PC keeps crashing for no reason. It crashes when I try to open an application and respond to one?

Sounds as if the removal took out a system file that the virus attached too.

First thing to try is to use the "System restore point" facility
For Windows 7, Open System Restore by clicking the Start button . In the search box, type System Restore, and then, in the list of results, click System Restore.

If that doesn’t work try the Windows Start up repair tool,
Press and hold the F8 key as your computer restarts. You need to press F8 before the Windows logo appears. If the Windows logo appears, you need to try again by waiting until the Windows logon prompt appears, and then shutting down and restarting your computer.
On the Advanced Boot Options screen, use the arrow keys to highlight Repair your computer, and then press Enter.

Microsoft also offers a free portable Windows Repair tool, this can be downloaded from the MS site or from the Major Geek's site, I would suggest you enter into Google "windows repair tool & go to Major Geek's & follow their Guide first hand rather than from me cutting & pasting it here for you!

If the above does not fix it for you, and I would be very surprised, then you may be looking at a factory reset. Before you do this last ditch action, remove all of your from your computer, either by going into safe mode & drag/dropping on to an external drive of using a Linux based rescue disc to gain access to your files.

Good luck & come back if you have problems or a clearer explanation.