I am having a similar problem with a Nadia installation on an Acer AX 1200 with Athlon 4850E and 3 GB, dual booting to Vista.
If I shut down properly, and leave the computer off for a period time (ie overnight) and choose the default linux from the grub menu either the video goes dead (monitor indicates there is no signal) or the video is scrambled with a black screen and about three or four lines of random color.
If I shut down properly and power back up after a minute or so linux boots as it should from the grub menu default choice.
After Mint failing to boot from default, doing a hard shut down, and powering back up, and choosing the Linux recovery option from grub, then choosing the resume normal boot afterwards always gets me back to a fully functional Mint.
I changed the grub to make Windows the default choice by changing the grub.cfg file as per instructions in this forum, Grub works fine if I leave everything alone, going to Windows and booting Windows normally.
When I use Linux recovery mode to fix the grub I get a message saying a file has been set to a future time and I should check the hardware clock. I checked the clock setting in bios and they are OK for my time zone (Mountain standard).
This is a minor PITA as I can always get into Mint by choosing the recovery option in grub, and I have to use Windows most of the time anyway (not because I like it so much
but it is bugging me.