The bike was functioning properly until recently, so it could potentially be that it is really dirty. I don't see how a longer axle would be needed because, like i said, it did shift fine.
FBinNY, I will try adjusting the inner limit screw while the cable tension is released to see what happens. I think she may plan on bringing the bike in, so I may not have any time to work on it anyway.
Thanks for your help, I'll update you if something new develops.