There's actually a maddening two-fold issue at play here, FrugalSaver. It probably has nothing to do with the SIM card.
1) If you're using iTunes on Windows, there may be driver issues at play. If they currently aren't, they probably will be soon enough if you're on Windows.
2) In addition to driver issues, there may be O/S software mismatch between the data backed up and the phone.
iTunes won't restore data to a device from a backup off of a build of iOS more recent than what is installed on your phone. This means you have to bring your build of iOS current via a forced update through iTunes, because it won't do an OTA update without a full setup first. You won't be allowed to update your phone to the current iOS build through iTunes unless you have the latest version of iTunes installed first. Under Windows, this sometimes causes device recognition failure and driver issues. If you run into iTunes not recognizing your phone at all after updating it,
this is the driver song and dance you'll have to do to fix it.
So:
1) Update iTunes.
2) Fix driver issues (if any).
3) Manually force update of iOS to phone.
4) Then and only then will they let you restore data.
Of course, if I'm misunderstanding what you're trying to do, just ignore me.