It really sounds like some major corruption problems. I suspect you both did the Upgrade Installation rather than taking the time to do a Custom Install. This works quite often, but when it does have a problem it often creates very strange problems. It depends too much on what's going on with the original OS.
It sounds like something did not install correctly. You could try a Refresh Install, but be advised any non-MS apps you installed will have to be reinstalled. (They are uninstalled during the Refresh)
A better option could be to reinstall from scratch. Did you originally burn a DVD or Flash Drive? If so you can just pop the media in and start over. Having a DVD also gives the option of using the Repair Console.
If not, your...