Either the wires are shorted, its a bad guage, or you need a new fuel pump sending unit. Lower your fuel tank and unplug the wires going to the pump and check the guage with the key on. If it still reads full suspect bad wiring or possibly a bad guage. To check the guage remove the instrument panel, find the fuel guage wires and test for voltage. I'm not certain on the exact numbers so grab a repair manual. If it reads empty unplugged then either the sending unit is bad or somehow the float luckily got stuck in the up position. In that case carefully remove the retaining ring, remove the pump and check the arm for movement. In that case it will unfortunately but most likely be a bad sending unit. Its very unlikely that its the arm stuck.
Search Buick Skylark Questions
Are you a UK consumer? CarGurus now has a discussion forum in the UK.
Buick Skylark Experts