If all you are changing is the string that is the new computers name, you might be able to do a "search everywhere and replace." Type Ctrl-H or use the menu commands Search > Search and Replace.
For example, if the path to your media files on your old computer was C:\users\computer-old\documents, you might be able to replace this everywhere with C:\users\computer-new\documents. Of course, replace these example phrases with the actual path to your media files.
I recommend you experiment/ practice on a copy of your database until you're sure you've got it right.