It sounds like you have a bunch of viruses on the computer, and if you wait until AFTER you suspect they are there to download antivirus software, it will also be affected by the viruses.
It used to be that if you bought anti-virus software from the store, that you could boot from it and scrub your ailing drive of any viruses. I have gone soooo long without viruses that I do not remember how one would create a similar boot disc to do the same
Avast seems to sell one for like $10. Here is one from Kapersky that seems to be free:
http://support.kaspersky.com/4162 You definitely want to download and create the disc from a separate computer, and THEN boot up your computer to let it scrub. If you have trouble booting to the CD drive, you can start hitting F12 during start up to display the boot menu, or you can alter your BIOS boot priority settings to make your CD/DVD the first bootable device. Look for the 'hit any key to boot from DVD' message and hit enter - or some other key.
Anyways, I hope that helps.
When I remove viruses from people's computers I take their physical drive and plug it into my computer, which then sees it as a data drive, which means that any viruses on it will not boot up into my memory. I then use MY Avast antivirus software to scrub their drive.
At any rate, you have some things to check into and decide. I DO think that weird behavior like that is an indication that you have some 'critters' in your computer.
Bob Bone