When I read your post while in the middle of downloading the 6.1.3 update, I immediately cancel it to avoid similar issue with your 4S but I could no longer cancel the update despite removing the wifi connection and it stuck the update in the middle. I have no choice but just continued the update. Fortunately, my 4S works well and there is no problem about wifi connection and bluetooth. Please try to switch off and on again.
Backup to iTunes.
Export your Camera Roll to your desktop.
Restore as new (not from backup).
A) If the problem ιnsists must be hardware issue.
B) If not, try to restore from backup that was done right before the 6.1.3 update.
B1) If Wi-Fi works you are done. (Delete the last backup that you done in iTunes and make a new one. If you try to restore from the last backup you will "restore" the problem.)
B2) If not, you have to restore as new (not from backup) and re-setup your iPhone.