Ubuntu may not boot up because grub may need updated. Does Ubuntu show in the Grub Menu?
To solve that; while your booted into Linux Mint run this cmd as root:
I don't know why Mint is the only distro that will boot on that HP.
Some installers don't have the option to try the distro first and place you right into a fresh install.
Is your HP a UEFI machine?
Is secure boot disabled?
I've had similar issue's myself.
My Sony Vaio will only boot Centos, Fedora or Debian.
For some reason I have not be able to get any other distribution to boot.
Another thing; it could also be that the machine only recognizes 3.0 usb's and not 2.0's.
-::-I suspect it could be something proprietary or perhaps a UEFI issue.-::-
Is this your wife's machine?
http://support.hp.com/us-en/document/c04094869
I'm not an expert with the UEFI EFI partitioning.