Lillian - First to you have a working battery installed? This camera will go into lockup when the battery is to low for it to function.
It's also possible the battery contacts have also corroded check the onboard battery tester to see if power is getting through. If you find the power is present and the shutter will fire off but the mirror won't come down it's possible the foam rubber bumper the mirror hits at the top edge has gotten sticky from age. Using your finger nail give a very slight pull down (very little force needed here!) to see if that frees the mirror. If it does then you'll need to get to a camera repair shop to get the foam bumper replaced.