Welcome to Android Central! Was this S3 originally purchased from a carrier store, and if so, is it still on that same carrier's network? Carrier-specific phones need to be on that carrier's network in order to get official system updates. Since you're not getting any mobile data service, that would prevent the phone from getting any system updates. Contact your carrier and ask if you need a replacement SIM.
Also, the S3 is very old, and it is highly unlikely that you have any official system updates waiting for you.