The battery shouldn't have much of an effect on the signal. If you are losing a signal you can try to perform a master reset on the phone. This will help with your signal if it's the network.
Menu>Settings>Advanced>Connectivity>Master Reset: When it tells you to "Enter Security" press in six 0's. > 000000
If it is not the network than perhaps the phone it's self is the issue.
i do not have the option to create new messages or check them i cant receive on the phone or...
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i do not have the option to create new messages or check them i cant receive on the phone or internet but i have unlimited eerything plan