Sadly, i've seen this all too often... and it looks like moisture damage.
Dark spots are where things shorted out. So, what now? Glad you asked.
It all depends on, if you want to keep everything stock, or if you just want it working again.
Answer to both is replace power supply.
(1) Stock: Find part number and search on google.
(2) Make it better than new:
STOP! - - - !!! UNPLUG POWER FROM WALL FIRST !!! - - -
Locking plug with 3 wires is your line input 120-240 volts, 50-60 Hz. Center wire is ground.
Red and black wires, cooling fan, maybe? Please, see where they go.
This only leaves your small plug with ~7 wires. Now you may need some help. One of those
wires turns supply on. Some go to ground rail. Others give regulated voltage(s) to system.
Ok, i searched, system name only, with not much luck. Start by carefully removing bad supply.
Look for any stickers or writing on outside case. Snap some pictures of anything you find.
Post them here, and i will see what information i can dig up. Fingers crossed, pin-out of plug.
Please, for your sake, don't start poking wires in holes, or try to hook up an ATX power supply,
without first learning what each wire is for, and voltage requirements on them.
Come back soon, and i'd be glad help.
Good luck.
- David C
Almost missed blue and white wires soldered in lower right. Follow them too, to where?