What is the ruling on allowing one's brother to use the computer for committing acts of disobedience, and is that considered participation in sin?

You are not permitted to allow your brother to use the computer if you are certain or highly assume that he will use it in a way that is Islamically impermissible, due to the Almighty's saying: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression." You should gently and kindly advise him to fear Allah and stay away from prohibitions. If he does not respond, then do not allow him to use the device so that you do not become an accomplice in sin.