If you detach the cable from the derailleur will the derailleur move all of the way across the cassette?
If so then the problem is with the cable, cable housing, or shifter.
When you say lowest do you mean smallest cog or biggest cog? Technically the lowest gear is the largest cog on the cassette.
Follow the instructions for adjusting derailleurs found at:
http://www.parktool.com.
Al