LM 14 Cinnamon live cd ( not a new 14.1 ISO ) use gallium llvmpipe software rendering , but after installed will use Mesa DRI rendering. see : http://blog.linuxmint.com/?p=2234
I don't know if 14.1 ISO will correcting your problem. I didn't have intel GMA 3600 to try.
You can try add nomodeset to force software rendering .
while booting, hold shift keys until grub option appeared . press "e" to edit.
insert line : nomodeset
after quiet splash
press ctrl + x to boot
update : i read a lot of people cannot boot aspire one D270 to ubuntu 12.10 ( LM 14 parent ), but boot with software rendering to ubuntu 12.04 ( LM 13 ). see : http://ubuntuforums.org/showthread.php?t=2074161