|By the sound of it your computer is badly messed up, so the safest bet would be to backup your important files then either do a factory restore or windows re-install.|
The alternative is to wait and see if anyone has time to spend several hours with you on here going through the whole system in the hope they can clean it properly.
There is no need to run without an Antivirus and it is asking for trouble. Microsoft themselves do one for free (Microsoft Security Essentials) and there are other free alternatives which are good and are not trials, such as Avast, AVG and Avira.
Always pop back and let us know the outcome - thanks