Have you been able to burn in the past with the same hardware and software? No, you don't "need a separate power supply just for the burner." But, it may help not to do any other tasks on your computer while trying to burn a CD. In fact, I believe that will give you the best chance of getting a successful burn and should be the normal practice when burning; just let the computer do that one task when you've started burning.
What is the power rating, in Watts, of the power supply unit in your computer? Were these two drives added after you bought your computer? Did they replace older optical drives or were they additions to your system?
Have you experimented with changing the burning speed? What speed were you using when you tried to burn? You have both a CD burner and a DVD burner, right? And, you have not been able burn with either of them, right? Are you sure you're using Nero correctly? What happens when you try to burn? Do the process appear to start and then stop, or what? Do you get an error message?
