Well first check to see if the cables to your HDD are plugged fully in. Then like what was already stated about the DVD drive. Except if possible, try to use the same cables off the DVD drive. To help rule out a faulty cable(not likely). If you can't, then just try a different port for your HDD.
If that doesn't work. I'd take off anything that doesnt need to be there to run. Basically MB, CPU, Video Display, then that HDD that isnt turning on. Everything else leave off. If this works, then add 1 part at a time and test. Might be your PSU is faulty or the 1-line from the PSU that powers your HDD or adapter.