Re: Laptop won't power on when not hot / on AC.
You may not need to go far out to the stores.. If you still can't find one try get a free pre-paid credit card, type it in google and type your location, should bring up shops that have access to these cards, I use to use one but I've not since years and years ago, they was great for purchasing online gifts and things I wanted.
And since you said it's under the CPU, I kind of feel sorry for you, I'd be carefull around this area
Goodluck with the laptop, hope you get it fixed