Computer Woes

When you tried the second computer, did you use the same outlet the first one used? I'm wondering if you had some sort of power surge come through since they both got knocked out.
 
Power supply, motherboard, or CPU. If it gets power and all the fans spin up but it doesn't nothing (and you've ensured the monitor works), it's probably the motherboard. If nothing spins up and you push the power button only to find literally nothing happens, probably the power supply. If it was the HDD that wouldn't stop it from trying to boot up, it would get to a certain point and tell you there's no boot drive detected.

And never use a normal vacuum cleaner around a computer, for sure don't actually vacuum parts off.

Hey this is actually good and pretty common advice about never vacuuming. I never used to follow it though and occasionally vacuum the dust off my motherboard but weird stuff does happen, I lost a couple sound cards I believe to vacuuming and the one time I really learned my lesson was when after a vacuum the computer wouldn't boot properly, RAM problem, I thought one of the RAM sticks was screwed but both worked when tested by themselves, turns out the motherboard can no longer do RAM in dual channel so I'm still using both but not in dual channel mode.
Also if your swapping graphics cards and pulling out RAM sticks it sounds like you have enough know-how to build your own PC in future!
 
a couple of thoughts if you haven't already tried them, replace the bios battery. for a couple of bucks, it can help. There should also be a "reset" button near the bios battery, give that a poke if you can find it. power-supply testers can help, but note that you need to know what to expect, as some power-supplies will test as though part of them is dead, but really they don't have that capability at all. A brick and mortar compy store should be able to test that if you just bring in the power supply.
I think you definitely dealing with different problems. Like RevDevil I ran into a machine with a dead power button, and that was all that kept it from starting properly, as the button sends a signal, not like a light switch as most people think. That machine had really weird start-up problems.

when you push the start button, does the cpu fan twitch? do any of the fans twitch? If they do, then you are getting power to the MB, and it just isn't starting up. before every test, unplug the pc from the wall for a minute, as it lets you start from scratch, a single charged capacitor can change how it is starting up, consistency is the key.

Just to be sure, check that the power supply switch is on, if it has one (yeah, kinda a dumb thing that you've probably looked at, but I've missed it before as well)
In all the switching around, double check that you have all the wiring harnesses plugged in. they can work loose, and again, I've done it too

You may need to think about replacing. I'm not much of a windows fan, but I've yet to have a totally irreparable failure on a PC, and the only time I had a mission critical machine fail, it was a mac. Buy to your needs, not to a brand. (you may want to look into somewhere other than Dell, personal bias there)
 
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