Have you tried changing your video driver, since it is X which crashed?
Do you get to a terminal login, or does it just stop? When you run the recovery version from GRUB, what happens? Also, what desktop version and processor version are you attempting to run?
In Mint Update manager, are you only installing the higher priority updates, or letting ALL updates occur?
LMDE Mate 64-bit, LM16 Mate 64-bit
Debian Xfce 64-bit, Xubuntu 13.10 64-bit, Xubuntu Trusty Tahr 64-bit, Antergos Xfce 64-bit, PCLinuxOS LXDE 64-bit