TriggerFinger

If you are sure on the health of the RAM sticks, try stripping the laptop down. Leave RAM, mobo, and LCD (just make sure you leave the part that has the switch/power button). Power ON. if it behaves the same remove the LCD. From there you can conclude it could be the motherboard or not.

With an open laptop check the cables that plug into the motherboard. Make sure each one is plugged in securely.

Once the laptop is stripped down and is powering up without shutting OFF a few seconds later, put each part back one at a time. Power ON the laptop each time you put a part back. Start with the keyboard then the hard drive, the CD/DVD drive, Wireless card (if any) and modem. Of course you can do it the other way around whatever is convenient for you.