Then it is possible that the board on the DVD drive has a short in it or a blown surface-mount fuse if all of the connections to the DVD drive are secure. Eliminate the DVD drive and change it with an one that is new see if that actually works. If it will, you are able to either change the complete drive, or look for an alternative board.
Bad motherboard
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 try this without getting 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.