I am having exact same issue. Upgraded to iOS 5.1.1, then restored as suggested by AT&T so that phone can be offically unlocked. But I see SIM NOT INSTALLED error, even when I insert valid SIM. can't even use it as iPod touch for music apps on WI-FI. I am stuck. Let me know how to at least activate without SIM.
Same issue. I bought mine from a Radio Shack. They got it ready, transferred info from old to new and home I went . It started showing the No Sim card installed message fairly soon. When it happens I can text but not receive or make calls. Haven't had it long enough to add more than a couple of apps...and they were same as on old phone--so I have no experience with how it interferes with or is connected with any apps.
The only fix I've found so far isn't permanent. Restart phone. And for a while all is well. Was hoping I could find a cure on this forum...but not so far.