I had this similar problem, but with a netbook, which has always been finnicky and now just does not draw power. I looked up the instructions for replacing the power supply, and the power source is basically the first thing they put in, so the process was something like 63 steps long. In the end, I just ended up putting a windows partition on my other secondhand laptop that I only use for questionable internetting and lending that one to my roommate. I realize that that story leaves a lot of detail out, but there it is.
Anyway, I had a similar problem with a phone, and the issue was that the USB cable had gotten borked when a cat had repeatedly knocked the phone off the dresser. I recommend trying another cable. --- Willis, it seems like every other time you post, I need to look up a word that's in the OED or Urban Dictionary but not both. -Mimir
The basic idea to taking apart a laptop and putting it back together is to use a piece of paper and put the screws on the paper in the relative positions they were in, so you're sort of making a diagram on-the-fly.
Use multiple sheets of paper to represent the different layers.
Put everything back how you found it.
Don't force anything too hard. You might find there are some plastic clips in there and you want to wiggle parts free if they're clipped, not break the clips off, because then you're going to have loose fitment when you put 'em back together.
It's not really that hard if you're brave and especially if you're cheap.