As I remember, these use tantalum caps, so they are unlikely to be bad.
I used to repair these, but it has been many years, so I don't remember what the current drain problem (rare) was. I do know that working on SLRs requires much more than the usual "handiness" that many people have. Unwise use of solvents, brute force in opening, or even just touching some things can cause expensive damage.
You can get a service manual online (e.g., ++https://www.manualslib.com/download/704000/Canon-Ae-1.html)++.. If you are up for it, give it a try. You need electronics troubleshooting skills and equipment as well., Go slow, patience is your friend. If you take it to a camera repair shop, make sure it's a good one. Those are thin on the ground, it really depends on where you live.