For the most part there is little problem using a computer for people with hearing problems. Almost all of the output is visual. There are some situations where sound output is used though. For these, the problem can sometimes be worked round by using visual output instead.
By tradition, computers go `beep' when some program sends them a special code. This is generally used to get attention to the program and for little else. Most of the time, it's possible to replace this by making the entire screen (or terminal emulator) flash. How to do this is very variable though.
for xterm, you can either change the setting by
pressing the middle mouse button while holding down the control key,
or by putting a line with just `XTerm*visualBell: true' (not the
quotes of course) in the file .Xdefaults in your home directory.
The console is slightly more complex. Please see Alessandro Rubini's Visual Bell mini HOWTO for details on this. Available along with all the other Linux documentation (see section other Linux documents). Mostly the configuration has to be done on a per application basis, or by changing the Linux Kernel its self.