F2 means there’s friction on the mechanism -some rubbing. You need to disassemble the fan to ease it. Instructions are on ifixit and work. Good idea to have a light lubricant handy for the shaft also.
I found that "F2" meant that there was some resistance inside to the fan spinning. Disassembling it again and removing any friction resulted in the fan working fine with no error messages.
Thanks for the great instructions. I replaced the battery in the old 3G and got concerned only when reconnecting the cables’ tiny plugs. Clear and concise layout!