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When yo say restore as new, I presume you mean clicking restore in iTunes, letting it do that, and the restore my backup afterwards?

How do I ensure it puts the latest build on the phone?
 
When yo say restore as new, I presume you mean clicking restore in iTunes, letting it do that, and the restore my backup afterwards?

How do I ensure it puts the latest build on the phone?

No. Do NOT restore from a previous backup after it finishes. Pull in your contacts, apps, music, etc after you select set up as new.

Download this: http://appldnld.apple.com/iPhone4//041-3417.20111215.Slnt4/iPhone4,1_5.0.1_9A406_Restore.ipsw

And hold shift(or option if you're using OS X) and click restore in iTunes and select that firmware.
 
Cheers.

I should mention though that the firmware already is 9A406 and the Invalid Sim message was coming up after I restored the phone last night, plus both before and after I restored my backup.
 
Cheers.

I should mention though that the firmware already is 9A406 and the Invalid Sim message was coming up after I restored the phone last night, plus both before and after I restored my backup.

It's because your BASEBAND in Apples servers is set to a different provider. I had this problem and went crazy after going through 4-5 iphones. Finally I found a topic on Apple forums that this was a issue after having a phone replaced. My phone baseband was set to Korea on Apples servers and they fixed it but it took a few days once the REP figured it out. You must speak to Tier 2 support. They are the only ones that will know how to resolve this issue. You will need the serial # for your original iphone that was replaced. Hope you have the box. It's the only way they can figure it out.

Not AT&T but Apple is who you need to call and tell them you are getting invalid SIM every time you get your phone restored. It's because Apples system is setting your phone up for another provider/location/country.

https://discussions.apple.com/thread/3375290?start=255&tstart=0
 
Got th brand new phone yesterday (and the free exchange phone).

Everything fine so far with the new (WHITE!) one.

Using original sim.
 
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