Windows XP Home Edition help me!!

My desktop has started to do the following:

When I turn on the power button it will boot up and when it gets to the user password it turns off the computer.
If I unplug the computer and leave it unplugged for awhile then restart it, it will boot up and work until I try to run the antivirus program (both AVG and Onelivecare safety scan) the program starts to run then turns off. (turns off means instantly, without a normal shut down) If I turn on the system it will reboot but turn off as soon as I get to the user password again. and again and again

I have checked all the connections, cleaned out the tower and removed all the dust, replaced the internal battery but don't know how to get an antivirus program to run.

Any ideas as to the problem?   

[Moderator]

Try booting to safe mode and running the av from there - can you do that?

My F keys won't respond, I can't get to the safe mode boot screen. I can get into setup screen by pressing the delete key

[Moderator]

Is there an "F-Lock" key on the keyboard? If so, use it to toggle the F-keys and then try again. Otherwise you'll need to try a different keyboard. If you still can't get to safe mode, use msconfig's boot.ini tab and the /safeboot option.