Why won't my laptop boot?

Why won't my laptop boot?

OK, I got a fix-it laptop as payment for helping a neighbor with her computers for a while, and it needed a new motherboard. I spent 3 days taking it apart (first time I took apart a laptop, so it took a bit), waited 4 more days for the new motherboard to ship here, put it in and spent until nearly 11:00 PM (8 1/2 hours) putting the laptop back together. I had plenty of trouble both taking it apart and putting it together, but it's together now. Well, almost together, I skipped a few screws to get it running and test it faster, because I wanted to save a bit of work if it still didn't work.

Now it's running perfectly…for about 20 seconds at a time. I start it up and it runs perfectly, but somewhere in the boot process the screen gets static like antenna analog tv with a bad signal, but it gets the static in color, then the computer just quits like someone unplugged it.

It seems to turn off at random points too. Sometimes it does it after only 10 seconds or so, once it even got to where it has that turning blue circle and says 'Welcome'. (It's a Vista.)

I was wondering if you guys could direct me towards where I should look for a problem. I'm assuming it's some loose cable somewhere but I really don't want to take the thing back apart without knowing what I'm looking for. Laptops are hundreds of times more complicated inside than any desktop…

It's an HP Pavilion dx9000 Entertainment PC if that helps any. Anything else you need I can get.

Oh, yeah, I tried plugging in an extra monitor that I know works and the static happens on that one too, so it's not a problem with the monitor.