iPhone 4S Battery
After seeing the comments about trouble finding the carrier, I shut down the phone, did a soft reset (by holding the power and home buttons until it started and then shut down and stayed off), and removed the SIM. After the repair, I replaced the SIM and plugged it in to the charger. It started up and found the carrier (Verizon, as it happens) immediately. I would guess that only the soft reset made a difference, but I did both.