iPhone 4S won't charge or connect to iTunes through cable properly.

Hi, My iPhone 4S is not charging or connecting to iTunes. Only very sporadically does it charge properly or connect to the computer. It is always charging a bit however when the cable is connected, but very slowly (approx 1% per hour). On the odd occasion it does charge properly it all seems fine, but this is very rare.

I have tried several different cables (all original Apple ones). I have tried charging on different power sockets. I have tried charging on different computers (both Apple and Regular). I have also tried charging on a docking station.

I am taking it to an Apple support center this Friday, but urgenly need to sync with iTunes to save all my apps I have bought. I have not synced for a while. I have been told I will probably get a new phone, that is why everything needs to be backed up now. I have already back-up my setting on iCloud, but as far as I am aware this will not back up the actual software.

Please help. I am desperate!

Thanks