Dell Inspiron M5040 Shutdown Problems

I have a just-over-the-warranty Dell Inspiron M5040 which is driving me batty. I'm running Windows 7 Home Premium. Here's what's happening, and what I've unsuccessfully tried so far:

1) Browser windows open and close automatically without going anywhere, sometimes with random strings of numbers typing into the browser bar. Start menu opens, random numbers type, menu closes. WMP settings open and close. Windows Security Essentials is turned off, and will not restart. Finally, the computer just shuts down. Sometimes all symptoms happen at once, sometimes just one or two, and sometimes the system just kills itself with no warning.

2) WSE, SpyBot, and MalwareBytes detect no problems. I've run GMER, and it detects no MBR problems. I've seen the symptoms persist and replicate in Safe Mode, no networking. Also, symptoms persisted in two different states, connected to two different routers. I have a second, older Dell laptop connected to the same wireless router, and it's never had any of these problems.

3) I reinstalled the factory OSR, and symptoms persisted. I did a clean install from disk, and symptoms persisted. It's possible personal files were infected with something, and that they reinfected the clean machine when I installed them from a flash USB drive (although I don't have any executable files on that thumb drive).

Any insights or ideas would be appreciated. I've considered a bad fan, failing PSU, faulty keyboard, etc; but the full cocktail of symptoms seems to me to point toward some sort of persistent infection that's eluded my best efforts to date. I'd love to find that I'm wrong and need a component replaced, but I'd love it even more if I could just figure out how to fix my machine.

Thanks in advance for any advice you may have.