From computer #1: Save the brushes from the Brush Palette menu (the little black triangle tab), name it something relevant, i.e., My Brushes.
On computer #2: Place the new brush library (My Brushes.abr) into Program files > Adobe > Photoshop 7 > Presets > Brushes.
Launch Photoshop, go to Brush Palette Menu, "load brushes". Choose "My Brushes" and go!