Yeah, DO NOT MOD the PSU. Voids any warranty, has the potential to ruin the performance of it. And it's about like messing with the back of a CRT monitor if you don't know what you're doing.
Nothing like a good 5-10amps at 10k-20k volts to remind you how mortal you are.
Now as far as having them powered by the PSU, that's just a matter of wiring the leads to a 4pin molex connector. Just make sure the LED's are rated to run off 12v power. Otherwise you'll need to throw a resistor into the circuit to lower the amount of current going through.
You know this just made me have the idea of possibly modding that old Antec, or Lian Li case that I use to use. Through together an LED layout that would make it look like one of those old computers you'd see on TV with all the useless lights. Either that or set up the LEDs to make it look like it's changing colors inside the case. I've got all the 555 timers and other things laying around that I'd need to be able to pull it off.