Usually to clear the BIOS you'd have to apply the jumper to the opposite pins, not just remove it though. I've run plenty of boards sans jumper, but hey def worth trying. Good spot!
If that doesn't work, I know you've tried some of this already - just want to make sure all the below has happened concurrently
1. Take the motherboard outside the case and put it on top of a piece of cardboard or an anti-static bag.
2. *Thoroughly* inspect the motherboard on both sides - looking for any little bits of loose wire/screws/metal/etc that might be causing a short.
3. Install 1 single stick of ram in the blue slot closest to the CPU, and install the CPU with the stock cooler.
4. Leave all other components out - hard drives, optical drives, extra ram, video card, etc.
5. If you have a spare PSU (or one in your own rig maybe?), use that to power the mobo. If you don't, use the PSU you bought.
6. Try booting into bios, and keep an eye on the temps while you wait for it to possibly crash.
It'd also be worth running memtest on the ram sticks if you have another spare machine around - unlikely that a faulty module would be causing this particular issue but stranger things have happened.
