Yesterday I had to disconnect the monitor from one of my PCs. All I did was disconnect the VGA cable from the bottom of the monitor and then move it.

Today I reconnected the monitor but it won't find a signal. I hooked the monitor up to my other PC, and the monitor worked fine. I connected a second monitor to the PC in question with a different VGA cable, and still got no signal.

I have cleaned and reseated the RAM sticks and checked everything to see if anything was loose. Still no dice.

The fans only spin for about 10 seconds after I boot the CPU, though I have no idea if that is normal or not.

To my knowledge, I didn't even touch the CPU when I was moving the monitor. However, it is possible that I jostled the CPU and knocked something loose since I was installing a heavy window AC unit in the general vicinity. That may have something to do with my current problem, or it may have nothing to do with it at all.

Help?

How old is your monitor? Also what type of monitor only VGA or is there a HDMI port too? When you monitor is unplugged does it say something like no vga/signal connected? Could be a vid card problem

The monitor isn't the problem. Your computer is failing to POST.

Remove and reseat the video card.
Remove *any* peripherals. Just monitor & power
If it still doesn't work remove the memory and try to power on. It should beep.
If it doesn't beep, remove and reseat any other PCI/PCI-Express cards
If it still doesn't work/beep remove every card except video card
If it still doesn't work/beep remove video card - It should beep when you power it on.
If it still doesn't beep, unplug any internal devices (harddrives, cdrom, etc)
If it doesn't beep, replace memory and power on
If it still doesn't beep then you're getting into rough seas.
Remove any internally connected ports, like front panel USB/Firewire/Audio
Could be PSU or motherboard or CPU.
You can try removing & reseating the CPU but
a) You'd need to reapply thermal paste and have high-purity rubbing alcohol to clean off the old stuff
b) I've never seen a CPU become unseated

You can also try clearing the CMOS on the board. This will wipe out any bios settings and should give a clean(er) slate.

I haven't heard any beeping at all when I've booted. I'll try all those steps when I get home.

Did all this and more, basically following every POST-fix guide I could find on Google.

Turns out my motherboard is fried. Booo.

You get an A for effort. At least it failed catastrophicly instead of causing occasional blue screens and lock ups that confuse and infuriate you until you've replaced every other part in the system