i would open it up to check a wire didnt get knocked loose, but it probably is that the motor just died. honestly if the motor on yours is original its lasted a lot longer than most. those vibratory motor’s usually die after like 8-10 years.

while you are in there checking for loose wires get the actual part number off the motor and you should be able to find the correct replacement with that.

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.

Swapping out the pump should be relatively straightforward. One thing you might consider when buying a new pump is getting the brass version (Ulka EX5) that many have said reduces noise. There's also a higher wattage version (52W instead of 41W) of the same pump that has higher water debit and can give you more flexibility which is the one I got for my machine (Ulka EAX5)