I'm just trying to check if my Nokia Lumia 920 has specific battery problems or not:
1) It takes about 2-3 hours easily to charge. Is this normal? My old Galaxy S3 used to charge much faster. (Charging through wall socket)
2) My battery doesn't last at all on 3G (Maybe 3-4 hrs). I'm thinking this might be due to poor 3G signal as the battery is decent on 2G connection. [ I have disabled most apps through background tasks, NFC is always switched off and I quit almost all apps instantly)
I generally don't use WiFi on my Lumia 920 (I have LTE in my area), but I leave Bluetooth on at all times so that it always works when I get into my car. Even with that, I easily get a full day's worth of battery (usually two days, but I always recharge at night given the chance). Recently, the cell tower near work has been having issues (including on iPhones and Android phones, so it's definitely the tower/AT&T), so my battery life has been struggling a little bit more at work, but I still easily get a day's worth.
Occasionally, I have noticed that my battery is randomly just destroyed in a matter of an hour or two. Whenever I notice this, the phone is also noticeably warmer than it is during normal inactive times. The normal app to blame is anything related to GPS, but I usually do not need to use my GPS (if you do, then make sure you close it by opening it and hitting Back until it closes). The other day, I noticed that it was happening every other day even when I wasn't really doing anything, so I actually uninstalled Skype. That seems to have fixed it; perhaps it was coincidental, but it seems like Skype was doing something in the background and eating the battery.
If none of that works, then you should probably go return your Lumia 920 and pick up a new one.