Starting trouble

Hi I have an 89 Toyota Camry it starts fine and runs fine but after you have been driving it for a while when you turn it off it doesn't want to turn back on the lights turn on on the dash and the seatbelts engage but it won't even turn over if you leave it for 30 minutes or more it will start back up again I looked under the hood in the fuse box and noticed the 80 amp alternator fuse was blown I'm not sure if this has something to do with it or not