iPhone 3GS network problem!

I have a 3GS that was working ok, a while ago, the network signal was dropping a lot then always "no service", tried to change the connector and the antenna, then it started rebooting if i insert a sim card when i first turn it on, then i discovered tht if i plug it into a charger the signal comes back and i can make calls!

Is this a battery problem or something else?

Note: tried another battery (not new but in good condition) but same thing!

Any suggestions?