Hey guys I might have a solution:
I had the same problems with my 4s: weak signal strength no 3g connectivity at all! and on top of that itunes wouldn't restore my iPhone..not even iOs 6! (after checking with apple it would say that the building wasn't right for my iPhone...even though it was the same file, downloaded trough iTunes from apple, I used to update from 5.1.1 to 6)
Except for yhe iTunes problem, for which I haven't cheked if it's still there, I solved the 3G connectivity problem and the weak signal, and the battery is improved too!
That's what I did:
- I had iTunes make a backup on my computer,
- than I reseted the iPhone: settings--->reset---->delete contents and settings
- I had iTunes restore my latest backup
- after that I waited until iTunes displayed the battery fully charged
- I turned off the iPhone(while stil pluged in)
- I kept it off trough the night
And in the morning I had no more signal strenght problems or 3G connetivity issues!
I hope this works for you too! let me know!!