From the info provided, it sounds like the power supply has issues, and that is the best place to start to trouble shoot this, as it is the least expensive replacement. Just because you have some power does not mean you have correct power.
Start by trying another monitor on that machine and that monitor on another machine with secure connections. If that is OK we can rule out the monitor as the issue.
Do you have another known good power supply you could slip in for a test? Are you planning to repair this yourself? Do you have a somewhat geeky friend who could help?
Other possibilities are malfunctioning hardware - RAM, motherboard, hard drive, etc., but let's start here.
I don't think the compuiter is dead, and certainly all the data files can easily be retrieved in a variety of ways. I don't think leaving it on overnight brought about this problem.
We'll await your response to the above.