Disassembling and replacing the flippers under the playfiled the first time seems/feels like a scary task, but after you do it once you'll be a pro.
First thing I'd do is pull your pf up to working position, grab an allen wrench and disassemble the flipper mechanism. Once you do that, there is a plastic sleeve that sits in the coil. It should flow out from inside that coil easily. If it does not, you probably need a new coil (these coils last of pretty long time, but in these older machines, It's not unusual to have to replace them, and they're not that expensive). If you look at the coil, it will have a specific number printed on it, and most pinball companies online will have a replacement for you. Additionally, these same companies will have flipper replacement packs specific to your era of machine. These packs will replace all the pieces including a new coil sleeve. Additionally, the small piece of metal that has a round piece in the middle of it, the coil stop, is probably flattened. These packs will have everything you would need, including a new coil stop.
The first time you do it, it may take 30 minutes, but then you'll be a pro and it'll take a little bit less than next time.
Based on the age of your machine, I'm just guessing that the flipper mechs probably never been replaced /repaired, and a new setup will probably bring your flippers back to life!