You should just go ahead and get rid of the car. I'll take it off your hands, if that will help!
Seriously, what bullitt99 and Super Blue 72 have suggested is right on. You want to isolate the problem to either the sending unit, the gauge, or the wiring/connections in between. (You seem to have checked the gauge and found it to be OK). Their suggestion to ground at the sending unit will help you isolate where the problem happens.
It is possible that the sending unit is bad, or that there is an open circuit somewhere in between the sending unit and gauge.
Good luck!
Tom