First thing you do in that 20 min window, is go to task manager and pretty much shut everything down but the main things. Access(if possible) the security on IE and your OS and put everything on high security(annoying, but it's only for a little while). Then go download Kaspersky or something similar, a quality antivirus, download the free trial and scan like hell. This should get rid of the virus that actually shuts down your computer. Also download the free trial of superantispyware(a very good anti spyware), that should get rid of those pesky popups.

If one or all of the above isn't possible, reformat your computer. Usually already installed on hard drives, just restart and go to your OS setup(by pressing F10 or F3 or whatever, should be displayed). It is advised to totally reformat(clean the hard drives), but if you can't, create a seperate partition for your old hard drive so it can't come in contact with your OS.