"just fixed my 4S (at least for now) after replacing battery. After plugging in to charger, I got the dreaded plug into iTunes symbol. After trying to restore numerous times to no avail, I plugged back in the old battery. I was than able to do a factory restore. replaced the old battery with the Ifixit battery again and it is working so far.
"I had this problem on a non jailbroken iphone 4s tried the above to no avail .
Basically if you've exhausted all the other fixes... changing the battery,removing firewall,antivirus,editing host file etc etc. Then check the last line of your itunes restore log if it says something like...'RamrodErrorr domain/3ea: update_gas_gauge: gasgauge_swupdate returned -1' ... Ifixit has the answer and more details here.....
Small component broken from the logic board .
In my case on a (very)close inspection it's a capacitor.. that's missing!?!.
Hope this helps someone as this info took me best part of a week to find!"