I am at a loss as to how to save my computer

This is a problem that began the evening of December 27, 2014.

It began while I was on line with Internet Explorer. As it happens, I was on the Yahoo website.

Two things are happening.

First, I am getting multiple repetitive warnings that Avast Free has blocked malware. The details are different malwares each time, but each appears to end in “iexplore.exe” in the description.

I attach some examples.

Second, the screen briefly goes blank several times, I get warnings about the display driver, and then I get a blue screen and which says something about a “memory dump” and then the machine reboots.

The blue screens usually happen when I am web browsing but not always.

Also, web sites are slow to open.

Avast Free is up to date; Malwarebytes and Spybot find nothing wrong. I do get CCleaner alerts that I have over 2 GB of data to clean.

When I switched to Firefox I still get multiple virus warnings; the bluescreens occur as well.

I also got several blue screens when I was not on any browser.

I also attach screen shots of the recent Avast history; I cannot seem to copy the data as a document.

I am at a loss as to how to save my computer.

Dell XPS 8500. Windows 7.