This is actually a pretty complicated problem with not enough detail to know which one of many things is causing the failure so I'll go over some basics:
- Your phone needs to be activated
through iTunes after a restore - so
something in that restore process
didn't work.
- The sim and phone have three components - any of which can fail.
- The activation process is complicated and has a lot of checks to be sure the image you are installing is not modified so that the phone will work as designed. This activation needs to connect to the internet so even when everything under your control is correct, it still fails from time to time. Problems on your computer with iTunes or the system itself can cause this to happen on an otherwise working phone.
I'm also going to assume the phone is locked to AT&T to keep things simple. If the phone is unlocked legitimately through the carrier and officially recognized by iTunes' activation process this is much more complicated. If it's otherwise modified, the complication is really much more involved so I'll leave those out of the discussion.
Looking at #1 above - the best advice is to reseat the SIM card and then try again to make sure it wasn't a timing or contact alignment issue. Considering #3 above - it's simplest to take your device to a totally different computer and try the restore there - you can always take it back to your computer to put the backup on it once it's working.
Let's look at #2 in more depth - sim and phone. A bad sim will cause this - you'll need to get another SIM to test this and replace the SIM with one active from your carrier if it's the cause.
Have you tried another SIM from your carrier - it doesn't have to be attached to an active contract or active line - it just has to be working. Try to rule out that the sim itself is bad or has failed. A good SIM will get you to "waiting for activation" and a full restore so you can copy apps to the phone and otherwise use it on WiFi. Putting your SIM in another phone can help know that your SIM is not bad, but it has to work in your phone, so you may need to get another SIM even if yours works in another device.
Once you rule out the SIM - you'll need to rule out software. Do another restore of the phone following this knowledge base article. If that doesn't work, force the device into restore mode to get the software loaded properly. Be sure there's not a failure in the restore process or you'll be wasting time on SIM olympics or getting your phone swapped.
That's the third part of #2 - if your phone has a failure (dust or dirt, contact problems, moisture or corrosion on the inside that is causing the circuitry to break, or just a random electrical failure) you will need to get it in for service. There a technician will have the tools (otoscope, test rig, test SIM, good software to restore your device) and the training to know what worn contacts look like to know if it's a cleaning/reseat issue or a hardware repair is needed.
iMessage can also register email address (like your Apple ID), that's how it works on iPad and iPod Touch.
So it's completely normal to be able to send iMessages with an SIM-free iPhone.
As long as you are connected to a WiFi network.
Best Answer
Restore that iPhone. If the problem persists: take it to a repair shop. It is probably a hardware problem. I had the same problem myself.