You main problem is your PSU could have shorted out your motherboard and just about everything else in the PC, however you really wont know until you get a new PSU.
Replacing the PSU is easy, just unscrew the 4 screws on the back of the case which hold the PSU in and disconnect everything its connected to. (motherboard, graphics card, hard drive and cd drive should be the main things)
Then its just a case of re connecting the new PSU to everything that the old PSU was connected to, remember most motherboards will have the big 24 pin connector and a smaller 4 pin connector to power them, its easy to forget to connect the 4 pin connector.