I've come across a handful of customers that had the following scenario:
iPhone1 is stuck in a cycle of rebooting during startup.
iPhone works perfectly fine if restored to factory settings.
Restoring the iPhone from a backup causes reboot cycle to return.
If you're having this problem, we've had some successes removing the problematic settings files from the backup2 so you can still restore your photos, app data, etc. Send us an email through our support page (and feel free to mention me, Kelly, or this post directly.) We can try out some of the fixes for your backup!