NO - That old PC can't run VISTA effectively without some/many hardware upgrades. Also Microsoft has very good control over the copies of VISTA. Immediately after you install a second copy it will start bugging you to register and two weeks later it will shut down all the good parts of VISTA if you can't register it with a valid (unused) key. It's a 12 year old computer that has outlived its design life. All the parts are living on borrowed time. Use it until it fails and then be sure to recycle it.
It all has to do with keys. You do not have a valid key to go with the Vista DVD. The only key you have is printed on the COA label on the bottom on the laptop it has been used (and registered with Microsoft) and will not be valid on any other computer. I would wait for Windows 7 due to be released later this year. It fixes the major problems with Vista and might run just fine on your desktop.