My parent's computer has stopped working. It is on, but is not doing
anything (the monitor is not receiving a signal). It will not reboot
or even shut down via the buttons on the front.

I need to figure out what the problem is and whether it is fixable.

I was planning to redo their hard drive soon as it was orginally
partitioned into 4 sections of 10GB each and the C drive is basically
full while the other drives are not. I have already transferred as
much as possible to the other drives, but it is now full, mostly with
windows files and things i am not sure I can move. My plan was to copy
all their files to my external drive (plenty of room), and totally
redo their hard drive. Their computer is older with only usb1.0, so I
have not finished copying all of their hard drive. I've been doing a
section per night and letting it go for hours while it transfers the
files. It was NOT doing this when it died.

Any suggestions that might fix it? I know it is older, but it has done
everything okay for them. They don't need anything fancy. Could they
just need a new hard drive or power supply?