I had built a computer and it was working fine. However as I was about
to close the case while the power was on and the computer was running,
some of the  power supply cables that were not being used hit the CPU
fan and the computer went dead. How do I fix my computer?

There could be an easy solution or a difficult one, depending on what
was damaged.   So, to start, you should clarify what happened and what
happens now:

Did the fan break the wire insulation?  If so, which colored wire(s) was it?
Did the fan itself break?  Did it stop working before the computer crashed?
What do you mean by "the computer went dead?"  All power cut off?
Do you get any power when you try to turn it on (PS fan, CPU fan, etc)?

For about 15 bucks, you can replace  the power supply and see if that
works.  Otherwise, you may have caused a short on the CPU or
motherboard, which could have possibly damaged almost every component
in the case.  But let's think positive.  Good luck with that one.  Oh,
and make sure you unplug the power supply from the back of the
computer before you do anything.  with an exposed powered wire, you
could incur some unwanted side effects.