Is it permissible to wipe a doorknob and a computer with a single cloth moistened with madhiy (pre-seminal fluid) without purifying the cloth between the two wipes, and what is the ruling on what is touched afterwards if it is not permissible?

If you touch an impurity while your hand is dry, the impurity does not transfer to what you touched. If something is ruled impure, it is purified by pouring water over it. Wiping is sufficient for purifying smooth surfaces according to some scholars. The default is that impurity does not transfer in case of doubt, and one should not open the door to obsessive doubts in this matter.