Hallelujah! My replacement cell phone is up and running. The original one was not charging, so my two batteries were both completely depleted. The new one is charging the batteries with no difficulty, and my info is restored from backup.
I was able to put one of the recharged batteries into the old phone, and it turned on. So I did a hard reset on it so that when it's returned, it will be back at the original factory settings. I didn't want to send it back with my phone contacts, personal information, and apps installed on it. (*cough*WMWiFiRouter*cough*).
So all is well now, and the Gremlns are exorcised. Hooray for getting problems resolved!