Have you tried replacing the battery? Does it have the IMEI number? You can check that by locking and then unlocking the screen, and on the slide to set up screen press the little circle with an "i" in it. If it doesn't have the circle, or it doesn't show the IMEI number, i'm afraid you have a baseband problem, but first of all, i would try with the battery, and if that doesn't work, do a full restore in iTunes in DFU mode (google for how to enter DFU mode on an iPhone if you're unfamiliar with that)
Have you tried hard resetting it? (WARNING: it will wipe all your data, make backup, if possible) This is how to perform hard reset: Turn off the phone, remove and reinsert the battery, press VOL +, HOME and POWER, and when the screen turns on, release POWER, but keep holding the HOME and VOLUME + keys until you see the green android (recovery mode), then using volume keys, navigate to wipe data/factory reset option, and select using HOME or POWER.