Use the Add/Remove feature in Control Panel to uninstall both. Now reinstall Word 2002. If you have a backup copy of your 2002 normal.dot, you can open Word to create the normal.dot, make a valid change that will affect the normal.dot (such as adding an AutoText entry), then close Word answering yes to save the normal.dot. Now you can replace the normal.dot with your backup and you will have all of your shortcuts.
When running two different versions of Word on the same computer, the oldest version has to be loaded first. This is one reason why you are having a problem.