I asked about the install so I would have some history on the machine--I do
not advocate a fresh install until all reasonable measures have been
pursued.  It is my experience that an install over the top of an existing
system rarely cures a problem and often creates more problems.  You can do a
clean install without backing up--don't format the drive and just install
W98 to a folder named other than:  Windows.

How to Install Windows 98 Into a New Folder
http://support.microsoft.com/?kbid=193902

I left part of my question out about the scans--I already knew from your
post that you used the products.  Do you update the definitions for your AV
and Ad-Aware programs before using them?  As silly as this question seems, I
have fixed a few computers that had these programs installed but the users
never updated the definitions and that was the problem with the machine.

I would look at a couple of possible causes.  First, go to device manager in
safe mode and delete (all if there is more than one)  your display adapter
driver.  Reboot and install the driver that you used previously that worked
correctly--it could be the latest driver is not suitable for your machine.
Next, disable power management in the BIOS and Windows and see if that
helps.  Finally, try a clean boot to see if there is a program running in
the background that might be causing the problem.

How to Perform Clean-Boot Troubleshooting for Windows 98
http://support.microsoft.com/?kbid=192926

If none of this helps and you don't get a solution from another poster, then
I would try an install to a new folder.