If the burner worked in the other computer then the burner is probably good. The probem more than likely is the drive select jumper on the back of the drive. What you do is look at the old drive that came out of the computer and see where the drive select jumper is located. Where to look? Easy on the back of the drive it is a small section next to where the ribbon cable plugs into, there is usually a number of gold pins in 2 rows with a jumper on them. And there should be some markings etched into the case right over the top that have letters like MA, SL. You have to determine if the old drive was a slave or master. Set the new drive to the same thing. The ribbon cable will have either an odd colored wire like red on one side of it or the wire will have a little ridge, this is pin 1 If the connector has a locator tab in the one side it doesnot matter it is located automatically.
When this is set properly one way you can tell this is when the power is turned on and after the computer goes thru initial boot the drive will open and close when the button on the front of the drive is pressed.
Hopefully this will work.