If the existing computer works then can I suggest you keep that as it is
The stuff you have been given can form the basis of a new job to be built at your leisure while you can use the existing for web access and anything else you use the computer for.
click here will give you a good idea of how to go about it
Don't be in a hurry.
Scott Mueller's upgrading and repairing computers from the local library might give you a heart attack, but the cd at the back of the book shows how to do it
Anything else, just ask here
Build ATX form factor buying a new case with power supply from Novatech or Dabs. You don't say what operating system the old computer has, but if you buy windows xp oem at the same time as the case, graphics card and memory for a new computer you'll have a system to last you for years