If I had to hazard a guess, I'd say you have memory problem.

You can try this for starters. You can find more detailed instructions in the manual:

1. Power off, unplug
2. Press/hold power button for ~15 sec
3. Open case and remove motherboard battery
4. Press/hold power button for ~30 sec
5. Carefully reseat RAM modules in their slots
6. Use canned air to blow out all the dust bunnies
7. Reinstall* motherboard battery (right-side-up!)
8. Close case and see if it boots with only mouse, monitor and keyboard connected

*If battery is more than ~2-3 years old, this might be a good time to install a new one. CR2032 3-volt lithium ion battery, ~$2 at discount stores.