I've posted several times about trying to install LMDE onto my new HP Envy 700-056-216. I finally did it.
HAVE A BACKUP COPY OF YOUR WINDOWS 8 OR 8.1 SYSTEM ON DVD'S OR A 32 GIG FLASH DRIVE because you will wipe Windows 8.1 completely off the computer.
1) Burn the iso DVD and leave it in the drawer
2) Reboot the computer and keep punching F10 until the BIOS appears
3) Enable Legacy and Disable Secure Boot, also disable the Function keys (All in the 3rd column)
4) Keep EUFI enabled, but put the dvd/cd at the top of the second column
5) Move to the first column and save the changes.
6) Reboot and the LMDE iso should eventually show up. Install from the "compatible" mode (2nd entry down) (this can be a long wait)
7) During the install, delete ALL of the partitions except the UEFI boot one. (You will need it later)
Create a "swap" partition and an ext 4 one for the root.
Then let it run.
This will not work if you wish to keep Windows 8.1 on your computer as trying to add it into the grub menu will screw things up and you will not be able to get back into LMDE.