I have one that looks practically new. Everything works well but that frame counter is stuck past '36', meaning that it kept acquiring higher numbers until it could not go any further.
I would like to know where the tiny lever is that releases that counter back to zero. On most SLrs there is a tiny lever where the back meets the body, but I could not find one on this body. As you know, on this body, the entire back is removed (no hinge), but I still cannot find that release lever. Thank you, in advance. - David Lyga
You probably have a broken clock spring!
As others have already said, there is a round (usually silver IIRC) machined and domed sprung button under the take up spool. As you remove the back, it should drop down, move a couple of levers and release the ratchet so the frame counter returns to start, or -3 before zero. From memory (like 25+ years ago) on one camera body I had, the actual button was sticking slightly. The other 2, (one owned by the photography center I worked at) the clock spring in the counter had snapped, meaning there was no force to return it to the start.
Oh, and clock spring? Like a spring in a clock, or watch. A long thin piece of spring steel, anchored at one end on an arbor, and anchored at a static point at the other end. Then wound up to exert some rotary force when released. (Can you tell I've had a couple of cameras in bits today?)
Many are anchored by bending the spring into a square/angled shape both ends which fit into anchor points on both the arbor and static anchor, some are spot welded in place. I honestly can't remember for the F but I can have a look in a couple of days though!. The frame counter cover however, is easy to remove by undoing 3 tiny screws and a circlip for the actual dial. If the spring is only bent into an anchor, it will have probably broken at one end or the other, so you should be able to bend the newly snapped end into the existing anchor with some small needle nosed pliers. If it's broken somewhere in the middle, it's time (ha!) to find a local horologist or watchmaker. They might be able to help make a new one.
I do remember (at the age of 17 or so) ordering and receiving two brand new frame counters, with a new clock spring attached, from Nikon. I think they were less than £5 each! Ahh, the 90s, the time when you could order new parts for Nikon's oldest SLR...