Mysterious laptop problem - powers off suddenly / doesn't turn on

A couple of days ago, my laptop started powering off suddenly. One second it's on, and the next, no hard drive activity, no screen, no nothing. This happens in an instant and without warning (no blue screen). Starting yesterday, the problem got worse. After the power cut out, I would have trouble starting the computer up again. Sometimes it worked, sometimes it didn't. When it did work, I sometimes got as far as the Windows login screen. When I hit a key to begin typing my password (or swiped my finger on the fingerprint scanner), the power cut out. Today, it seems to have gotten even worse. Sometimes the startup process doesn't even get as far as the Windows login. A couple of times today, I pushed Power, got the the Windows Startup Error screen, selected to resume Windows as normal, and bam! Power's off.

Now, this gets even more mysterious. Sometimes I push the power button (after one of these instances), and nothing happens. Sometimes I push the power button, and the power light comes on, and then the fan, but no hard drive activity. Dead. Sometimes the computer won't start up at all unless I remove the battery, pull the plug, wait a few seconds, and then try again.

Even stranger... I have the computer on right now. It's been on for 5 hours, and it's working fine. I'm afraid to turn it off or put it to sleep, because I know it might not start up again.

If you are thinking overheating is the source of the problem, as of right now, after being on for 5 hours, each of my two processors is running at 53 deg. C and 45 deg. C, which I don't think is very hot.

I've been using computers for 25 years, and I've never seen anything like this. Any and all advice would be greatly appreciated. Thank you!

Specs:
Sony Vaio VGN-Z90US CTO: Core 2 Duo P9600 (2.8 GHz), 4 GB DDR2, 200 GB 7200 RPM HDD, 256 MB nVidia 9300M GS GPU, 13.1" 1600x900, Windows 7 Ultimate
 
You say it works when you take the battery out, do you have the AC adapter plugged in, if so it sounds like a battery problem get someone to check your battery out.
 
Sorry, I wasn't clear about that. The problem still occurs when I have the battery removed and run it on AC.
 
In that case it sounds like a motherboard problem take it to your nearest repair shop ask them to test the motherboard because to me it sounded like the motherboard had a slight fault but when you had the powercut it had an effect on the motherboard.
 
Thanks for the feedback. I do plan on having this looked at by a professional (unfortunately, not under warranty), I just wanted to try to determine if is definitely hardware related or not. If it is the motherboard, does it make sense that once the computer is on and running it works fine?
 
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