If you left something disconnected then your volume buttons and your vibrate switch would not work as well, as they are all on the same ribbon. If those functions still work, you may have accidentally torn the ribbon leading to the headphone jack. In that case, you will need to replace the headphone jack/volume/vibrate ribbon.
You may have knocked off a resistor around the battery connection while disassembling the device. There are 3 small resistors under the battery connection that provide power from the power amp to the battery to charge it. If those resistors are missing, you can try a jumper with some circuit writer, but most likely the logic board is no longer going to work properly.
You either didn't properly seat the connections for the antenna's, there are two separate ones for the 4S. The WiFi is on the top right of the logic board and the antenna for cell data is close to the battery connection. It has also been known to have a clear film on the back glass, causing it to get bad reception. Just remove this film and try again.
Battery issue. It is asking to activate again because the logic board is not getting enough power to "pull up" your information. Most likely after placing a new battery in the device it will work properly and all of your data will still be there. I would just buy a battery from this site.
Without looking at the inside of one, I believe what you are referring to is the antenna connection. You can either simply replace the charge port, which comes with a new one or you can remove one from an old charge port.