trek road bike puncture and then gears stop working advice needed?
The lever not clicking when moving makes me think your shifter could be broken, but that does seem like an unlikely coincidence.

Shifter broken test: The way to test this is follow the cable down from the shifter and at the first place where the cable emerges from the housing, put your left hand under the bare cable and pull on it so there is tension on the cable.  With your other hand, shift up and down.  The clicks may get more audible, and hopefully you can feel the cable tighten and loosen with each shift.  If you feel the clicks in the cable tension, your shifter is fine and you can move to the next steps.

Housing popped out of cable stops test:  The way to find out is first "shift" your shifter into the hardest to pedal gear to release cable tension, then follow the cable from the shifter down to the derailleur. 
Check that the beginning and end of all the little plastic-covered pieces of housing are in their cable stops (the metal cylindrical pieces attached to the frame that hold the housing in place).
If one of the housing pieces has popped out, pop it back in and it should shift again.  You may need to manually push the rear derailleur cage towards the spokes to release the tension so you can get the housing back in.

Cable slipped test: Another possibility is the cable has slipped and pulled through the derailleur fixing bolt (the bolt that attaches the cable to the derailleur).
In this case, you would again "shift" the shifter to the hardest to pedal gear to reduce cable tension, loosen the bolt, pull on the end of the cable till there is no slack and re-tighten the cable.  The shifting should begin to work again.

It should be one of those cases, although a piece of housing could have splintered and you'll see small wires popping out of it.  If so, replace the housing.

Worst case, take it to a bike shop :)