Antec in my experience has tended to be crap.. Can nobody remember their dodgy PSU series from back in the day that actually -was- killing things? "EarthWatts" or something? 12 YEARS OLD?! Either you are trolling or want things to last forever.. nevermind all this crap i wrote before i spotted that! Don't risk it! Keep it if you must for sentimental reasons but DO NOT use it to power another machine!! Get a new one, good ones are surprisingly cheap now!
If you have access to a digital multi-meter and know how to turn on your PSU without a board attached, that would be the first step. Check the voltage of all the rails to make sure they're all within spec! (Simple way is, with nothing attached to the DC side output, no drives, nothing.. Short the green wire to a black wire on the ATX connector, connect your negative/black DMM (multi-meter) probe to any black wire or even the metal case of the PSU, then poke the (assuming they colour code or you'll have to check pin-out diagrams) various positive rails and measure the voltages.. It would be nice if you had a spare PSU too. As for load test, that can be difficult with out the "proper equipment" which i do actually have, dummy loads, even an oscilloscope haha.. But a ghetto method i love to use: old lamp type christmas lights on the 5v and 3.3v rails, a car audio amplifier on the 12v output rails wired to a low impedance sub or pair of speakers.. You can use a clamp meter or several DMMs in ammeter mode to see what current you can pull before the PSU shuts off.. Awkward to do, but hilarious!
Does the PSU even still turn on if you connect the power on wire (usually green) to a ground (black) wire? Unless you have a ground/earthing issue in your home, messing with the DC side won't electrocute you.. Just please, please be careful! If you are in any way unsure, not confident or worried, DO NOT do what i've suggested!
Anyway, most PSUs have that kind of protection if they're not cheap crap. I had a Corsair CX750 fail due to a now known bad supplier of ferrite chokes and electromagnetics.. Over time it would burn up, it actually failed whilst i was running a benchmark after smelling bad for two weeks! (Yes, i literally left it to see what would happen, i was confident.. It didn't damage any hardware, didn't even blow a fuse or trip the socket RCD, it simply shut off! And after a long time leaving it, never getting around to returning it.. I attempted a fix by replacing the coil with another i hand wound, using one turn less and the PSU is now working again!
Hilariously it was still able to start with a crispy, fried coil..but would overheat and shut off quite quickly and pull an alarming amount of power with no load..yes, i was bored!) But i'm drifting from the point..
Motherboards can just fail for seemingly no reason if they happened to have a bad MosFET or three, an imperfection in a main ASIC or chip, etc.. I've seen the main ITE IO control chip fail on some which means they won't turn on or won't turn off, or won't reset.. Rare though! As i say, all but the shittiest awful PSUs have forms of protection, will turn off if you happen to short an output or pull too much current briefly (i again love car amps for this! xD)
If you need any other help let me know. A series of lamps at the right voltage can go a long way.. 12v car headlight bulb for the 12v rail, stick something you know is 6v on the 5v rail, etc.. Shame i don't live closer to come and tinker!
Edit: I should have read more before opening my mouth.. The PSU is 12 years old?! That probably IS one of the bad Antec ones.. Even if you think it works, throw that shit away and replace it! Lol.. I have even older PSUs here, but i know what i'm doing. For you, the 'safe' way is to simply replace it.. If you have some junk hardware you don't mind killing, plug your suspect PSU into it and see what goes bang xD I had a 10+ year old PSU here, in the past had been suspected of killing hardware.. After i tested and measured it, i found it was putting out well over 12v on the 12v rail (over 12.4!) had seriously bad ripple, even though all capacitors were fine and the protection no longer worked properly.. I could literally make sparks with the 12v supply, the fan would slow/cut put the PSU kept trying to pulse power! It was quite a nasty, cheap OEM POS from back in the day though, i suspect the kind that used to come with cheap cases..