You're supposed to connect both. I'm still new at this, but I believe the 24 pin one is for the motherboard and the 8 pin one is for the CPU.
Optical drives now usually connect with a SATA cable, whereas older ones connected with an IDE cable (which is what your old one uses). I'm not sure how often new motherboards have an IDE connection available - I know my new mobo has one IDE slot, but if yours doesn't you'll likely have to buy a new drive.
Though it's not all that big of a deal - they're really cheap, around $20-25 for a DVD burner off Newegg. Plus then you wouldn't have to run that monster of an IDE cable in your computer :-)