If you've the 7.10 liveCD you should be able to boot up and run in safe graphics mode.
As far as what to do next. Mount your hdd and start copying files to whatever media you plan on using for backup. I don't have Mepis installed on anything and it's been about 2 years since I looked at it, but it is Debian based so most of the commands you'd use in Ubuntu would work on Mepis.
Jim
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