I replaced the optic boards in one of my Happs 3" (tks again to you, RayB ... saved me a nice amount!) with those for the Happs USB/PS/2 kit, plugged into my XP machine and presto, magico ... no additional drivers required (nor mentionned in the documentation).
The OP says that the trackball was dead before ... so I must ask ... what, exactly, qualified it as dead ?