From MEPIS Documentation Wiki
Wikipedia: A kernel panic is an action taken by an operating system upon detecting an internal fatal error from which it cannot safely recover... Add-on hardware or malfunctioning RAM could be a source of fatal kernel errors during start up, due to incompatibility with the OS or a missing device driver. A kernel may also die with panic message if it is unable to locate a root file system.
NOTE: Before you do anything, be sure to back up any important data to another drive using the MEPIS Live medium.
If you have made some change in the recent past, try to undo it. Such a change could have been adding new hardware, using a new kernel, etc. If that does not help, you can use the MEPIS live medium to access the hard drive and try to fix the problem. See links below for detailed approaches.