Are you friction or indexed shifting? If friction, I don't know what the problem might be. However, if you are swapping freewheels and derailleurs, it is possible that the index of the shifters does not match the derailleur, or more likely, the freewheel cog spacing. Other than that, I am not sure.

If you can switch your shifter from indexed to friction and then try the bicycle, the problem might reveal itself.

I do wish you good luck with your problem.