Its the Logic board in the DVD drive.
A Logic board is assigned to a particular Motherboard. You can swap all the hardware except the Logic board.
Maybe this will help. You have console A and B. You want to put dvd drive A into B. Well, Logic board B has to go into dvd Drive A for that drive to play games in console B
The big thing that sucks here is Lite on and BenQ have different shaped Logic boards.
Really you probably just needed one part replaced in the dvd drive that wasn't playing games for you. The original one. It either needs a replacement optic or spindle motor
I could help you with this. I do offer repair services. Even on the RROD one you have. Probably needs the Gpu reballed.
And you can Flash drives like the other guy said. But really it would be easier to repair the non working part and keep the drives with their proper console. Flashing can lead to Firmware Security issues down the road.... then you're locked out. Unless you stay on top of your Flashing updates