Join Date: Feb 2009
Bikes: 2008 Mercier Corvus Steel, 2007 Trek 4300, ~1980 Takara Deluxe 12, 1985 Trek 620 (modernized)
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Are these grip-shift shifters? If so, I pity you. I swear some of those grip shifters are designed to be disposable.
Assuming it hasn't been left in the rain, make sure nothing has jammed the cable or derailleur. Dribble good chain oil, like Tri-Flow, into the shifter and try to free it up. If that doesn't help, you'll have to disassemble the shifter, and there is a good chance you won't be able to reassemble a grip shifter.