A few points, since you have 4 PCs with the problem I doubt that all 4 have problems. Or maybe they have but I would run and buy a lottery ticket
1. You installed Linux Lite via DVD I'm guessing. Can you boot the 3.6 Live DVD and check if problem still occur?
2. Can you do the same with a 2.x Linux Lite DVD?
3. Linux Lite is not in the officially supported distribution of UNetbootin. If the USB key was corrupted someone,
you could need to "low-level" format it (i.e. complete wipe not just reformat) before doing anything else with it.
4. Bonus, if the key works in a Windows computer, you could try using Rufus of something else to put the ISO on the key.
Good luck!
-TD