1. measure it
2. go to Home Depot and find one the same size
3. find the screws holding your current one in place, unscrew and remove medicine cabinet
4. insert new cabinet and screw in place.

I meant to add that it cannot be opened because the mirrors frame is blocking it.

What you see is how far it can be opened.

See above, but you will need to flip it around. It appears the door hits the frame around the big mirror. So the medicine cabinet will have to swing towards you, not ideal but at least it works.

Maybe the medicine cabinet replacement could have sliding doors instead of a swing door.

You could remove it and replace with a wooden inset shelf area. If you're not handy you could get someone to do it. It shouldn't cost much.

Can you remove the framed mirror (or pop the frame off of it) in order to remove the medicine cabinet? Then you could just frame in some shelves instead.

Just remove it and see what the situation in the hole is. You can put in some shelves as arley suggested above. Paint to match the walls in a semigloss. Alternatively, if you are very lucky, you will find a medicine cabinet that will fit the hole but will not have such a large mirror on the front. 1" overlap seems to be common.

Thanks everyone for your suggestions. I will post what we end up doing to it!!!! Any other ideas appreciated!