Definately remove and clean the fuel petcock, as any crap that is in the fuel tank has almost certainly clogged the strainer screen on top of the petcock.
I like to use a solvent, such as kerosene, to clean out a gunky fuel tank. Gasoline has too low of a flash point to be safely used as a cleaning agent. If the gas tank is too far gone to be cleaned with some solvent, rags, compressed air, and patience, I've seen replacements on ebay for as little as $ 15.00. I:I