I haven't dealt w/ LED's in a long time, but here is what I remember....
I would use the 5V instead of the 12V of the PC power supply. Then, throw a 1/4W resistor in series with the LED so you don't burn it out. (Remind me...don't normal LED's run on just 2-3V DC?) You may have to experiment w/ different resistor values to try to get the brightness just right, but start w/ a 1K or so. IIRC, led's are current driven, not voltage driven so just remember the ol' V=IR formula. Depending on the number of led's (and total resistance) you might have to keep an eye on the total current draw from your +5V supply.
There are some super-bright BLUE led's available that run on 5V...they are like $5 each, but might look pretty cool, depending on the button color.