Didnt your motherboard come with 2 80pin cables? If so, did you try one of those?
But I can't imagine that a DVD burner would require an 80pin cable. It's probably not UDMA66 or higher?
Does the drive show in the BIOS? Or perhaps try swapping to the other IDE port on the motherboard?
Last thing would be to double check the jumper. I assume it's the only thing on the cable, so either set it to Master or Cable Select. I've found that some drives prefer one or the other. Some will only work on cable select, some only on master. So if you have it set to Master, try CS.
EDIT: and especially if you went and got another drive and it still did not work, you either need to try other jumper settings, or the port is bad.