Is it a Kodak Carousel? If so, 99.999999% of the malfunctions are due to a nylon "solenoid tip" (the tip at the end of the plunger) breaking down. It gets waxy and brittle, and then the two tabs snap off.
I used to be a professional photographer, and my slide projector died, and I can't afford to replace it with equally good pro equipment, and I can't get it repaired as it is SO old and obsolete.
The symptom is easy to diagnose. When you hit the slide advance button, instead of smoothly advancing to the next slide, the projector goes "clunk" (once!), and does nothing!
It's a $50 repair. At least, that's what it was back when I was in the business. Probably $75 or $100 now.
Or, you can buy the nylon tip, and the rivet that holds it to the solenoid plunger (or, salvage the old rivet), and replace it yourself. Total cost shouldn't be much over a dollar or so for parts. (It was well under a dollar when I was in the business.)
It's a bit of a bear to get it in, until you study the "guts" for a while, and discover that you DON'T have to disassemble the whole mechanism to replace it. You only need to pull off the bottom plate from the cabinet (a few screws), and then wiggle the old one out, and the new one in.
I always viewed that as perfect obsolescence (from a manufacturer's perspective). Sell a product that's built like a Sherman Tank, with ONE single-point-of-failure, with that failure mode guaranteed to stop it dead in its tracks, motivating the owner to either pay a lot to repair it (flat rate at the factory), or, pay a lot to replace it. With scads of carousel trays filled with slides, the owner is pretty much of a captive customer either way.