My Nokia Lumia 920 is working, at last.
There were three problems - the first was the "No service" status of the SIM card. The second was that some SIM cards sent my phone into the eternal restart cycle. The third was a 4G SIM card maxing out at 3G speeds.
Before I start with what I've learnt: If you're having difficulty with any of these issues, stick it out. It took me 20 DAYS to get my Lumia 920 working. Granted, if there was something that could go wrong, it seemed to go wrong for me. It's got to be someone :-) Also, during this time I got to play extensively with an HTC 8X. Both phones are really good, as is Windows Phone 8 over a 4G connection.
Anyways, onto solving the problems:
- Cause: This is a consequence of a failed network registration , and seems to occur most often on upgrades from 3G plans to 4G plans. That means that the MSISDN and/or SIM card are incorrectly registered on the network. Consequently the phone can't determine which network to connect to, so can't register the SIM/MSISDN with the network.
- Resolution: Call up your network, hope you get someone with a long screw driver that can manually resolve this. Note that there are up to five services that must be registered to the SIM (I believe these to be voice, SMS, MMS, fax, and IP/Internet, but not sure)  .
- Cause: A specific cause hasn't, as far as I know, been identified. I do know, however, that it is either the SIM card, the manufacturer's firmware, the Windows Phone 8 (WP8) operating system, or a combination of any or all of these.
- Resolution: Insert the SIM card into a non-WP8 handset. Make a call and send an SMS. Ideally also receive a call and SMS. This registers the SIM/MSISDN with the network, which is what the Lumia 920 fails to do, and consequently causes the restarts. It also confirms that your SIM card works. I've successfully tested this using a Galaxy Note II, a Galaxy SIII, a Samsung Omnia 7, and a Lumia 800. My first attempt using this procedure failed. However, trying again about 6 hours later worked, and I now have a Lumia 920 that successfully connects to the EE network at 4G  .
Note that the SIM card type also seems to affect phones. In my previous post up I mentioned that in the UK a Phones4U SIM card resolves the restarting issue. This is correct. Their SIM cards are from a different manufacturer than the EE SIM cards, and do indeed resolve the restarts .
4G SIM card connecting at 3G
- Cause: Completely unknown to me.
- Resolution: Insert a 3G SIM card into the phone. Go to Settings > Mobile Network (UK)/Cell Network (US), and set "Highest connection speed" to 3G. Remove 3G SIM card, replace with 4G SIM card. This should now connect at 3G. Return to Mobile/Cell network setting, change to 4G, and it should connect at 4G. 
. Note that the typical use case for a "No service" status is when the phone is out of range of a cell tower, i.e. you're underground or in the middle of the Sahara.
. These are all techniques that have worked in many cases. I understand that they haven't worked in others. I've also been led to believe that Microsoft, Nokia, HTC and network operators from the UK, Germany and the US are working hard to isolate the causes of these issues, and will inevitably provide a software fix in due course.
 My Lumia is one from the first batch available in the UK. The network tried numerous times to tell me that there's a problem with that first batch, and to exchange it. Exchanges do not resolve the problem. I'm now using that same Lumia 920 from that is reportedly from the first batch to hit the UK, and it's working just fine(!). If your network operator is insisting that this is a hardware problem, let me know here and I'll see if I can share some references from EE. Not prepared to publish them to a public forum, because I got them in good faith and obviously won't abuse that trust.