I have the same problem with Windows 7 Pro x64 and CD Burner XP. I can burn fine ISO, Music disc, disc to disc, video disc... but I have the message "no compatible drive found" when I want to burn data. I also have LPDS DH16ABSH SATA drive.
I tested CD Burner XP on another computer that run Windows 7 Enterprise x64 and I get the same problem...
I don't think this problem is coming from the drive compatibility but a incompatibility between Windows 7 x64 and CD Burner XP.
In hope that someone in dev team will read this message and solve the problem with Windows 7 x64 !!!!