That is a bummer it took that long. I can imagine how frustrating that is. Here is a reference article below if that happens again.
iPhone: Troubleshooting activation issues
This is an iphone article, but the same steps apply to the iPad. If nothing works, it is time for the phone to be serviced! Either call Apple or take it to the Genius Bar!
iPhone: Hardware troubleshooting
Re: iPad mini battery drain!
This article has a lot of good information - Apple - Batteries - iPad
Also check out this article for hardware issues with the battery - iPhone: Hardware troubleshooting
Just type lock apps in the search bar in the app store and you will see a ton of different choices. I would read the reviews and see which one is the best.
if all of the steps in this article don't work, iPhone: Troubleshooting No Service, Just call Apple. They will send you a new one and you send the old one back in the same box.
Yeah if most any issue like that continues after you do a restore, and don't restore from a backup afterwards, Apple will replace the phone for you without any fees as long as it is still under warranty.