Thanks so much for the information. I will do what ever I can to try and get these memories off the phone. I can't believe I trusted this Android with my pictures. Live and learn
@octopus65 , I do understand your frustration, and I am certainly feeling your pain.
But it's not "Android's" fault. This could just as easily have happened with an iPhone for instance. In fact, ANY phone, whether Android, iOS, Microsoft, Blackberry or other can fail. ANY phone with a non-removeable SD card will store the pictures and video on the internal Flash RAM, and you would have the same options with them as you did with this "Android", to set up a sync to a cloud server, connect to your home PC and back them up there, or use an On The Go (OTG), USB external adapter to connect to an SD card or portable hard drive and back them up there. You could even have a similar failure with a Digital Camera if the images are stored on the internal memory. You could even suffer a similar loss with a removeable SD card if it were to become corrupted.
The fact that the phone failed is not a flaw in Android, but almost certainly a flaw with the hardware or possibly with a software conflict that corrupted the firmware. Either way, your data is still on the Flash RAM card on the motherboard and until you either do a hard reset and with it wipe the SD card, or you incinerate the phone, that data is still there and could be recovered. The issue is whether it's affordable or not.
I have done data recovery for many friends and clients, and in some cases it was a failed hard drive motherboard that caused their data to be unattainable. In those cases, I hunted down the exact same hard drive on eBay, bought it, removed the working motherboard from the known good drive and placed it on the failed drive, and through the miracle of modern technology was able to recover the data. So don't get rid of that phone. If it were me, I would seek another working Droid Mini, and I would swap the internal SD card by desoldering it and then float soldering the one from your failed phone onto the working one. It would be a tedious task at best, very hair-raising and would require a very steady hand and careful monitoring of heat and static electricity but it can be done.
There are phone repair facilities that specialize on recovering data from failed phones, and they may be able to do what I've described, but they will charge you quite smartly to do so. And even then, there is no guarantee, but if the phone is completely unrecoverable, that may be your only option left.
Here's a working motherboard for the Mini on eBay now. For $63 including shipping you could possibly save the data.
Verizon Motorola Droid Mini XT1030 Replacement 16GB Logic Board Motherboard eBay
I'm not sure under which RF shield the SD card resides, but I may be able to find out.
Here's a video showing the disassembly.