The cost associated with getting your 4002 in proper shape range from a minimum of $50 to a max of perhaps $300.
The main problem is that these fine machines are getting old and internal parts deteriorate at different rates. When they were new and set up properly, they stayed that way. But now, in spite of there dateless look, they are getting senior.
Your sound problem could be the stylus, as I mentioned, but it also could be the arm weight adjustment. If you are good with your hands, especially with tiny parts, this is a fairly easy thing to accomplish.
Also did anyone tighten the transport screws and if so, did you un-tighten them? If the suspension is lock down the sound your 4002 produces is going to be truly awful.
Also the lubrication that the factory put in your 4002 and now turned into something more akin to drywall than lubrication. This effects everything, but mostly the tone arm and its ability to go up and down.
You stop issue may well be a dirty contact, all of which could use cleaning.
The bottom line is your 4002 doesn’t appear to be in bad shape, but clearly needs looking after. If you can’t afford to have it serviced, either store it with your family until you are in a position to spend the required bucks to have it serviced, or if that is not an attractive option, consider selling it to someone who can take care of it.
Good luck with your 4002 and school.
Jeff