I switched the SATA cables to see if maybe there was something wrong with the one connected to my optical drive. Nope, my computer turned on okay but I still have the same problem with the DVD drive.
I used your suggestions, Friedman. The SATA cable connections are secure on both ends. When I looked in device manager, I found it only recognizes the Hitachi SATA Disk Device, which I think is my hard drive. It's not recognizing my optical drive like it's supposed to, is it? What should I do?