Either you don't have enough cable tension (doesn't seem to be the case since it other shifts fine) or your low limit screw is set too far in (most likely cause). Is it more difficult to select the largest cog than the previous one? That would be a certain indication that it's a limit screw problem. Back the screw out by 1/4 turn and the problem should go away.
Re: b-tension screw, so long as the upper pulley is close but not touching the largest cog, don't bother messing with it.