A bit of a different post here. Mainly because I had to dig through a few forums to get an answer of sorts. 

I have an Olympus OM10 I found in a charity shop about 10 years ago for £10 and never used. Ive decided I finally want to use it and knew it needed batteries. Turns out it only had one?! The viewfinder was black too which I thought was a little weird. Taking the lens off, it was obvious the aperture blades wasn't the problem. I could also wind the shutter and fire it too. 

I ordered 2 new A76 LR44 batteries and threw them in and hoped it may fix my issue, but it didn't. A little searching lead me to this: when the batteries die, the mirror locks up. The battery replacement didn't fix my issue isntantly. I pulled the lens off and my mirror was stuck up in the lock up position. I simply used my finger to pull it down and it fixed the problem. 

I had already fixed the problem but using my thumb to hold the mirror up to show what I was seeing

Mirror down and camera functioning perfectly