iPhone fails to activate after a restore
To be clear, when you're saying the phone doesn't activate, do you mean to say that the cellular service is unavailable on the phone?

If so, I would try two steps first, and if those don't work, there are some other options floating around.

1) Try ejecting and reinserting the SIM card. This forces a reconnection attempt to the cell service provider's network. Make sure you're in a location where you normally get service to ensure your location isn't causing the problem.

2) If, after this, your connections still don't work, try restoring network settings. I know this is a cliche suggestion, and you did just restore your phone, but I've seen it work a lot. This too forces a reconnection attempt to your cell service provider's network.

If these don't fix your problem, go to an Apple store and have them check the hardware on your device to ensure it isn't failing/dead. It's a free and quick diagnostic.