Just my $.02
Hello, I came across this forum after having the same issue with an F3 I just bought. I am new to Nikon 35mm and can't figure out what's wrong. Like you I took a few good shots then suddenly the display is all nonsenseŚwith the "-+" signs and giving either 1050, 1060 or 0 as the shutterspeed no mater if it's in auto or manual. Did you ever resolve the issue?
just get some PH0 screwdriwer, open the top, clean the contacts with isopropylalcohol and assmble carefully back.
If it helps before you try unscrewing things I have a .pdf of the Nikon F3 repair manual. It is over 40MB in size but if you want a copy PM me your email address & I will upload it to one of the file transfer sites for you to grab.
Good luck with getting it fixed.