Sounds like you have 8-speed 105 brake/shift levers, but you mention a new (2 years old) cassette. Is that also 8-speed? It needs to be if it's going to work with your shifters.
If you were using the original wheels, did you have a freewheel on there? And no way it matches up to the increments in your shifter.

I've got a webpage with a rundown of how I built up my Centurion Comp TA (1984 model) into a very nice new bike.
http://www.unc.edu/~cupery/pics/bike..._TA_repainted/