Startup problems with iPad3 after iOS8 upgrade

Our iPad3 has been only showing the Apple logo, no swipe bar, and then it fades to black upon startup. And if the swipe thing does appear, then it flickers and goes to black again when we try to swipe. After doing this for a few times, and finally getting a shot at quickly swiping, the iPad stays on.

We didn't do a backup when iOS7 was loaded. We also lack a cable to connect the device to a computer with iTunes. The iPad was a gift (used) and the owner forgot to give us the cable, and we never had issues before with upgrades. We've never backed up the device, using it primarily for the apps, never keeping photos or other media on it.

Any solutions for this? We'd like to downgrade to iOS7, as the iPad3 worked perfectly then. But in reasearching the subject on these support forums, find that downgrading is not an option (unless one has a backup. Which we don't.)