OK, a little more detail:

Shift up to the largest cog in the rear, stop the wheel, then shift all the way down without pedaling. This will release some slack in the cable. If there are any split stops at all this will allow you to remove the ferrule from them for even more slack. Grab the inner wire with your fingers and slide it manually through the housing. Does it feel sticky or buttery smooth? If sticky there's still friction inside and lubing may take care of it. If not, then replace. If it's smooth it could be your shifter.

You'll get all sorts of advice on how to free up a sticky shifter, but my method is to use a graphite lock lube available at most hardware stores. With the small straw provided, spray it inside the shifter mechanism until it is liberally dripping out the bottom. The solvent wipes out the gunk and when dry, the graphite lubes things up again and frees up the tiny pawls. It may take a few applications, but it's worked wonders for me.

In my dry environment I also use a non-aerosol version of the same product for lubing the cables (the thin consistency wicks inside very nicely and is not sticky when dry) and all of the derailleur pivots.