The blind and some print disabled use computers all the time without a mouse. On MacOS X and the iOS there is a built in screen reader called VoiceOver (started with a command-F5 on a standard keyboard function-command-F5 on portables. With VoiceOver running you can work the OS with no mouse, or for that matter even a screen attached. It also support a wide range of braille displays.
There is similar products for Windows but they are not built into the OS and some, JAWS and WindowEyes for example, can cost more than the computer they run on.
On on the whole this is a rather silly question which if the authors had asked the question "How do the blind use a computer?" would have been answered.
Gregory Kearney
Manager - Accessible Media
Association for the Blind of Western Australia
61 Kitchener Avenue, PO Box 101
Victoria Park 6979, WA Australia
Telephone: +61 (08) 9311 8246
Telephone: +1 (307) 224 4022 (North America)
Fax: +61 (08) 9361 8696
Toll free: 1800 658 388 (Australia only)
Email: gkearney@gmail.com