If you would give us the model number Compaq it would help us in recommending a drive for you. Installing an external dvd drive in a modern computer is very simple, since they plug in with a usb cable. But some older computers only had usb 1.1. You need usb 2.0 for an external burner. Any computer made in the last five years or so will have usb 2.0.
Installing an internal drive would depend on whether you need one with an IDE interface (the older style) or SATA interface.
So let us know the model number and we’ll go from there.
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