Originally Posted by
JeanSeb
Sounds like a cable adjustment issue indeed. I would start from stratch.
It sounds like you may have left the shifter in the 3 or 4 position when you tightened the cable anchor bolt. Also I'd make sure all the housings are inserted in the frame cable stops properly.
Let us know how it works out.

+1 If I read your post correctly, you can't shift onto the largest cogs (that is, into your lowest gears). If your limit screw isn't the problem, then it's likely that your cable doesn't have enough tension. Tighten the cable by the proper amount, and you should be fine.