Dear jgrad; It can be extremely annoying when a computer just simply won't turn on, both for people who use computers and those who have to repair them, as there are hundreds of different potential reasons why it just simply won't work.
In order to help you, I will need you to try a couple of things:
-Check your warranty. This is the first thing you need to check as it might just end tomorrow. Just in case.
-Connect the computer to an external screen --> see if you've got a spare HDMi/VGA/etc. cable lying around the house which you can connect to a tv or a monitor (if you don't have one, ask a family member or a friend if you can use their's). If it works, hooray! that means that either your internal monitor cable isn't connected properly or that your screen settings are wrong. If that doesn't do anything, then you might have other issues.
-Check the RAM. It's possible that one of your RAM sticks might have disconnected itself somehow. Most computers have a simple cover over the RAM which can be removed using a regular small (#1 or #0) philips screwdriver. You can remove the RAM by simply pushing the two clips holding it in place outwards (they're usually white), and the RAM should flick out at an angle. Don't forget to remove the battery and the adapter before doing this. Simply pop it back in by pushing it in at the same angle and then push down so that the white clips latch onto it again. Reboot your laptop and see what happens.
Now if that doesn't solve your problem, you might just be dealing with a fried motherboard, which is really annoying as it can cost a lot of money to get it replaced (even if you do it by yourself, you'll have to cough up at least $100), which is why you should really see if you can get it fixed under warranty.
Now if they do fix it under warranty, I'd recommend making a backup. Get a hard drive enclosure/dock to put your hard drive in for the moment and backup data on another computer or a family member's computer or a friend's computer.
Please post the results here so that I can help you solve your problem.
Good luck!
- Guavas