If every one of the connections to your DVD drive are safe, it is possible that the board in the DVD drive has a quick inside it or even a blown surface-mount fuse. Take away the DVD drive and change it by having a brand new someone to see if that actually works. You can either replace the entire drive, or try to find a replacement board if it does.
Then it may be a bad motherboard if the cables and the drive are not the problem that cause the DVD drive not to turn on. It is hard to check this without finding a motherboard that is new testing your DVD drive on a known working console. Then you will have to replace the motherboard if the drive still works on another board.