You got a dead pump. But lucky for you, parts are cheap and it’s pretty easy to work in these things. Search YouTube for Gaggia classic refurbishing or get more specific, there’s a ton of videos.

I’ve bought a few old classics and fixed them up for myself and friends. They’re pretty simple, you might want to take the opportunity to replace the boiler gasket and descale it while you have it open. If you’ve never done this before and it’s that old, you might be surprised how gross it is inside. You can buy a kit to refurbish them that comes with all the gaskets you need. I would also highly recommend preemptively replacing the thermostat. It just screws in to the boiler. I’ve had one short out and catch fire in a old one, now I replace them as part of the refurbish.