You may just be in a dead zone, but if you are having this issue in multiple locations you should contact VZW tech support.
for now, go to settings/wireless&networks/mobile networks and make sure data roaming is enabled(and make sure you disable if you travel out of the country or you will get slammed with a crazy bill).
Also, dial *228 and enter option 2. This may help as well.
As for your battery--if you are in a 1 bar area your phone is constantly searching for 3g, and this will eat your battery in a few hours. One solution i use is to turn off the mobile network while I am in poor service areas(and not using the data). There is a widget for this that makes it as easy as one touch.