MacBook Pro 17 inch will not boot up

My MacBook Pro 17 inch will not boot up. I already have replaced the battery and the charger, still no results. The only time it will boot up temporarily, is when I unseat and reseat the battery cable to the motherboard (battery is removable).

The laptop will boot up on its own, then there is a light blue screen and a bar on the screen showing the laptop booting up. Then the wallpaper shows up like normal, but will then shut down again and cannot restart the laptop.

I checked the RAM, the laptop did not beep 3 times, which is stated in the forums, the laptop would do if the RAM was bad.

I reset the SMC per previous instructions from someone that sent an answer to my problem. The laptop was able to boot up normally and stayed on until I shut it down, but would not turn back on. There is no noise, the laptop runs quiet, the fans are clean and run quiet and the laptop itself is clean inside.

I already tried using the advice from those that sent me answers to my problem, but nobody has sent me an answer that has resolved my issue with my MacBook Pro. Please advise.