both 'to freeze up' and 'to hang' are correct.
(1) Due to a processor glitch the computer just froze up.
(2) Oh no, my computer is frozen up! For the love of God, do something!
(3) Pressing too many keys at the same time may cause your computer to hang.
It is also possible to just say 'to freeze':
(4) A frozen computer shows no activity on screen and does not respond to any input whatsoever.
(5) Pressing too many keys at the same time may cause your computer to freeze.
*not a teacher*
Uh, I forgot, you could also use 'to crash':
(6) This vicious virus crashed my computer.
Student or Learner