Put it on the charger over night. It's not like you have to run these batteries down to nothing before charging again.
Other than that....Factory Data Reset (if you haven't since getting the update). There were a lot of changes going from OS 2.3.6 to OS 4.0.4 and a clean system is much better than an "updated in place" system.
No, for 3G, you choose CDMA auto (PRL) or GSM/CDMA auto(PRL). For all radios, including LTE to be on, you choose LTE/CDMA/EvDo/GSM/WCDMA.