All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is permissible to recite the Quran on the computer or on the internet or from anything in which it is written. The issue of reward is totally left to Allaah The Almighty. Apparently, however, there is no superiority for reciting the Quran from the Mushaf over reciting it on the internet. The reward may vary for other considerations, such as the reward one receives when he performs ablution for touching the Mushaf. For further information see Fatwa 91645.
Allaah Knows best.