I'm working on a bike where the right shifter was not working and I replaced it. it's a 7 gear cassette and the problem now is that the rear derailleur would not shift down past 3. When I manually I moved it down it stays there. It does shift back up all the way to 7. Shift down and it stops a 3 even though the shifter keeps clicking couple more times. Any ideas what is going on?
Detach the cable at the derailleur and see where the derailleur sits. If its not in line with the lowest cog you need to adjust the lower limit screw. This is usually marked with an L. Screw it out until the top jockey wheel of the derialleur is precisely in line with the smallest cog. Reattach the cable with shifter on gear 1. Then click up one gear. Adjust the tensioner on shifter and/or derailleur until jockey wheel is precisely in line with second cog.
Finally shift all the way to the top cog and screw the high limit screw until you just feel resistance. This stops the chain going too far and dropping into your wheel.
It may be that the there is either grit in the derailleur, a burr in the metal, or maybe the spring has been over stretched. If it is the last it may be from a time when something was pressing on the mech that stretched the spring out too far. It wouldn't mean that the spring wouldn't pull all the way back to its normal position, but it may not have the same force to do so as it did.
I would try to take the chain and cable off and move the derailleur manually and see if you have less resistance at the the lower(smaller) gears then that may indicate this. If it is just harder to move in this range then it may be grit/rust. May have to lubricate it with grease or something else that is appropriate for derailleurs.