When moving to a new computer here are the issues you will need to consider:

1)  Moving the GradeBook software program.
You may want to consider upgrading to the latest version since you have to
install the GradeBook software again anyway.  Upgrading is free if you have
purchased within the last year.  Otherwise upgrades are half price ($34.99US). 
Detailed downloading and installation instructions are here:
http://www.1st-class-software.com/cgi-bin/fom.cgi?file=14
If you choose not to upgrade you can make two installation diskettes
using the TOOLS - MAKE INSTALL DISKS menu option from inside the gradebook.
Take these diskettes to the new computer and choose START - RUN.  Now type
in A:\SETUP and then click on the OK button.

2)  Obtain an Unlock Key.
You will also need a new unlock key for the new computer.  Here are 
detailed instructions on how to get it:
http://www.1st-class-software.com/cgi-bin/fom.cgi?file=17

3)  Moving my grade files.
Your grades are the most important part of this process as they are not
replacable.  Carefully back up your grades to a new diskette.  Take the
diskette to the new computer that you installed the GradeBook on in step 1
and load the grades in.  Detailed instructions are here:
http://www.1st-class-software.com/cgi-bin/fom.cgi?file=25
Once the grades are loaded on the new computer you should print
out a comprehensive report like the Spreadsheet Grade Report and
carefully check that everything has been transferred correctly.
DO NOT REMOVE YOUR OLD 1ST CLASS GRADEBOOK INSTALLATION
OR GRADES FILES UNTIL YOU HAVE CAREFULLY CHECKED TO MAKE
SURE ALL THE GRADES WERE TRANSITIONED PROPERLY TO THE NEW
COMPUTER.