Ok shut down and disconnect the power supplies from these two drives temporarily and reboot.

You'll obviously get a an error message saying Primary disk not found, ignore that and have a listen.

Shut down and re-attach the drives and get back to us.

Ok I'd forgotten that when I installed the new hard drive it wasn't secured, because I don't have a way of screwing it in (not enough room). So I tried booting up with that hard drive disconnected and there was no pulsing. Looks like maybe I need a short screwdriver to be able to screw the drive to the casing.

On most cases one side will be easily opened to attach the screws.

This is a view of the side where the mobo is attached and the slots where you need to attach the screws.

It looks like I can only attach the hard drive underneath (it is the drive on the left in the photo), as they are placed vertically under the DVD drive.

This is not a problem because the double drive casing is a slot in and do you notice the single screw in the middle at the top?

Unscrew that and the assembly will hinge forward, simply lift it up once you have to remove it.

Really? Great, I never knew that! I'll try that, thanks!

It worked! There is still a slight pulsing noise, but it's bearable now. Thanks