Hard Drive Suddenly Full, Won't Boot

When I went to use my laptop last night, it had mysteriously turned itself off (I had just charged the battery). Upon trying to boot, it would only go to the screen with options like disk utility, start up disk, etc. It wouldn't boot in safe mode. I tried it from my external drive with time machine backups stored in it, but no luck there. I remmoved the problem drive and installed a different drive in the laptop which booted fine. I put the problem drive in an external drive case but it doesn't show up on the desk top. It shows up in disk utility but shows it being totally full (I only had about 1/3 of the space use, so no idea what suddenly filled the drive). The drive won't mount in disk utility (it is grayed out). How do I get the data off this drive???