I recommend testing your SIM card in a friend's phone to make sure that the problem isn't with the card itself, or with your account on the provider side of things. If you do this and confirm that your hardware is at fault, it will be very difficult to troubleshoot without some knowledge of electronics and antennas in general. First, check a guide to diassemble properly. This model should have a plastic antenna near the bottom of the phone, and two shiny, gold, springy contacts on the motherboard which make contact with the underside of the antenna inside the phone. Cleaning and/or resoldering usually will do the trick. This type of antenna rarely needs to be replaced because it is essentially just a piece of wire printed onto a piece of plastic. Poor connection is usually the culprit.
Also keep in mind, sometimes software glitches can result in "No Service" indications but it is uncommon in your particular model. If you can do a software update via WiFi and you have the same issue afterward, you can pretty much rule this possibility out.