Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we commend your pursuit of knowledge and your eagerness to seek what is lawful and avoid what is unlawful. We earnestly implore Allah to bless your efforts in this honorable way.
If you know for sure that your brother has bought the computer with haram money, then you should avoid using it. However, if your brother has a mixed income of halal and haram money and you can reasonably assume that the computer is not purchased with the haram money, then you can use it.
Responding to the question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states,
If you know for sure that your brother has bought the computer with haram (unlawful) money, then you should not use it.
If, however, you are not sure of this fact, then you are not supposed to rush to make such a judgment; for, as Muslims, we should think good of our brothers and sisters unless we have clear proof to the contrary. If this is the case with you and your brother, then you can definitely use the computer without any hesitation.
If, supposedly, your brother has both halal and haram sources of income and you can reasonably assume that the computer is not purchased with the haram money, then you are allowed to use it. If, on the contrary, you are certain that it has been purchased with the haram income, then you should stay away from it by all means.
May Allah make us all self-sufficient with what He has declared as halal for us so that we have no need to turn to what He has declared as haram.
Allah Almighty knows best.
Excerpted with slight modifications from www.islam.ca