Welcome to StackExchange.
It's a bit difficult to answer your question without knowing the make and model number of the shifter. On Shimano RapidFire Plus shifters, used on flat handle bars like you'd find on mountain bikes, the model number is embossed somewhere on the shifter, most likely on or near the handlebar clamp. Also helpful would be a picture of the shifter with the dust cover removed so the internals are visible.
In absence of more details, I've gotten together a few references for Shimano RapidFire shifter repair/reconditioning. The Deore XT is this type of shifter, and in 2010 the newest model number was SL-M770. It's not clear to me what you mean by "reset" so I'm going to assume that your referring to the action of the trigger returning to the start position after each move and click forward. Questions that need answers at this point are, is a click heard when the lever moves foward? Does the lever feel "free" or encounter any resistance after the motion forward? In addition, are we discussing a right or left side shifter? A left side shifter would only have 2 or 3 detentes (corresponding to one or two clicks)as it controls the front derailleur, moving the chain between the 2 or 3 chainwheels.
At any rate, the two big things to check: 1) is the pawl engaging the cogs (teeth) with each shift? This toothed wheel inside the shifter should rotate a set amount--enough to bring the next cog/tooth into position to engage the pawls--with each swing of the shift lever (as if you were shifting up the cassete (or multiple chainwheel if it's the front) from a smaller sprocket/chainwheel to the next largest one; 2) is the coil spring correctly engaged in the mechanism--it needs to be placed in the correctly wound orientation and the ends secured in the correct engagement holes. Using the other shift lever (as if to move down the cassette, large sprocket to next smallest), you should note the pawl disengage the tooth and the spring tension that successively builds on shifts up the cassette, release which moves this toothed wheel the opposite way. A crisp click is heard as the pawls engage the next teeth, stopping the spring loaded rotation. To summerize: note if the shift lever motion translates into rotation of the toothed wheel by the actions of the pawls engaging the teeth of the this wheel, and does the spring appear to build tension (the spring will not have a great deal of movement if seated correctly). The inference that it was in pieces is not encouraging. Lotsa small pieces that are very particular as to their orientation and connections inside the shifter increases the complexity as there's a few things to look for at the same time in a problematic shifter that hasn't been disassembled beyond dust cover removal.
Check out these links and edit your question with the relevant details.
RapidFire reconditioning: http://www.bikeride.com/rapid-fire-shifters/ A basic set of techniques to utilize when first encountering a hinky trigger shifter.
http://thebiketube.com/tutorial/diy-how-quickly-repair-rapid-fire-trigger-bike-shifters. The Bike Tube is a DIY site with this particular link discussing basic repair tips for a trigger shifter.
This youtube video
is good for observing the correct anatomy of the shifter guts and it uses the SL-M770 as the example.