Dell XPS 400 running Windows XP (about 3 years old) shuts off at will, usually after 15 or 20 minutes. Sometimes it restarts several times. Sometimes it just stops. The ff blue screen error message often appears: "STOP: 0x0000007E." Further message has more numbers and refers to caching and shadowing. Then, "Beginning dump of physical memory" message at bottom of screen. Sometimes it just shuts down with no error message. The inconsistency has me confused.
After checking Microsoft Help & Support I think it may be related to the new monitor (emachines E19T 6W) OR monitor driver(?) which we replaced a couple of weeks ago. They refer to incompatible hardware device or driver. How can I check this for a monitor?
We replaced the Dell monitor because it went blank and showed nothing. My brother says the old Dell monitor works fine with his computer. ??? It makes me think the problem was the computer all along BEFORE the monitor replacement.
Do we have several problems or is it all related? I've checked lots of your messages, but don't see anything like this.

Before buying a new computer, I'd like to know if this is fixable or not!! I am quite ignorant re. computers, but desperate to get it fixed, so be gentle and basic!