Do you mean MEP 14 Plus or MEP 2014 Plus? If you have MEP 14 and your Windows is version 8 or 8.1 then you need to upgrade MEP to version 2013 or 2014.
Yes you can - you need to install MEP on the new computer and copy all the video files, images, project files etc from the old computer to the new computer.
However there may be a gotcha depending on the version of Windows on the old computer and the new one - file locations changed when Windows Vista was released - if your old computer has Windows Vista or later then there should not be an issue.
The only issue you may come across is if you change file / folder structure and / or location - in which case when you open a project, MEP will give you a warning that it cannot find the files and you should point it to the new location for the file specified.