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When the fuel gauge is stuck on full, this is most commonly a sign of a faulty Fuel Level Sensor. It is mounted to the side of the fel pump assembly, located inside the fuel tank. The fuel does does not need to be removed, as there is an access panel located inside the trunk, for which you can remove the fuel pump assembly. It's not all "that" complicated of a job, however, care must be taken when installing the pump assembly as to not bend or harm the float arm that is part of the level sensor. Other possibilites for this poblem are, damaged or broken wires in the electrical connector to the fuel pump assembly, the PCM (on-board computer) and/or the instrument panel gauge itself. The sensor reports to the PCM, and the PCM sends that info to the gauge. Although, the most common problem will be the level sensor. These sensors have been a fairly big problem for GM vehicles for years.