|What do you mean when you say it won't turn on / power on?|
It won't start up at all, or it does boot but Windows won't load normally?
If it won't start up at all.....
There may be something wrong with the main battery and/or it's too old and/or you have a charging connection problem.
See response 1 in this:
Correction for that:
The jack in the laptop should move when you wiggle the plug in the jack.
should have been
The jack in the laptop should NOT move when you wiggle the plug in the jack.
A common thing that can happen with ram, even ram that worked fine previously, is the ram has, or has developed, a poor connection in it's slot(s).
This usually happens a long time after the ram was installed, but it can happen with new ram, or after moving the computer case from one place to another, and I've had even new modules that needed to have their contacts cleaned.
See response 2 in this - try cleaning the contacts on the ram modules, and making sure the modules are properly seated:
For a laptop, you must remove both its main battery and AC adapter before you do that.
See the Owner's manual for your model if you need more info about removing and re-installing the ram module(s).