Motherboard LEDs not flashing + Computer won't turn on?

My laptop GPU was beginning to fail (I'd see pink and green discoloration and fuzzy text when the fan started to work harder), so I took it apart to clean the fan (I was going to put thermal paste but decided not to), and I put the laptop back together only to notice that it wouldn't turn on. I noticed the LEDs weren't working, but the AC light was fine. So I took the laptop apart again and when I got down to the motherboard, while I was moving it off the bottom base and for about a second the power LED turned on, and then turned back off (I'm keeping the Laptop connected to the AC with 2 sticks of RAM in). I'm not sure if it was the motion that made it turn on or something else. Now I've been playing around connecting and disconnecting the power connector board and it won't work. I noticed that while the power cable is plugged in and the two cables from the board are connected there is a faint noise coming from the motherboard. I assume that means the Mobo is getting power. I'm not sure what to do, any advice would be greatly appreciated.

I'd like to mention that I have a HP DV6700 and the laptop is 5 years old. I've never taken apart this particular model and I used this guide for help: http://www.insidemylaptop.com/disassemble-hp-pavilion-d...