OK, so my first reply had a note that said a moderator had to approve it first (because I am new I guess) but then when I decided to donate to the site it just disappeared totally, so either neither or both replies will likely show up now.
Try new batteries, if the shutter can't fire it won't reset the winder and it stays jammed. Those batteries are available almost literally everywhere batteries are sold, and though they last a long time I carry spares since they are tiny.
If it does need to go in for service, unless you want it for sentimental value just replace it with a better Super A (Super Program) which can be had cheap and has some key useful features added, otherwise send it to Robin: http://harrowtechnical.co.uk/ 50 pounds is about what a good CLA costs in my experience.
You can get a working camera cheap, but I don't trust any 30 year old camera unless its had a CLA to replace all the foam and bumpers and had its speeds all checked.
I could go for pages on why Pentax is an excellent choice for film cameras if you like.