Didn't Raimy already state that he had Windows running on the 750 in this machine? If so, it will almost certainly take a 500 in the second drive bay. Still, best way to be sure is to pull down the specs or get tech support to vet for you.
If I were going with a magnetic hard drive (as opposed to an SSD), I'd make sure it was a low-power 7,200 RPM drive. Since you already have a drive on hand, research it and see what it's power requirements are (most 2.5 in. drives these days don't draw a whole lot of power, but check anyway... better safe than sorry.
The power supply for that Alienware sounds massive! Most laptop power adapters are not half that capacity. (I upgraded my D620 to the nine-cell battery pack and already had a 90W adapter instead of a "stock" 65W, just for comparison.) That oughta be able to tote all but the most power-hungry drives, really.
Some vendors (HP is especially strange about this) use interposing connectors (adapters) to allow for easier insertion and extraction of laptop hard drives. If you need one of these and don't have it, it can turn into an adventure. Look on the old drive that came out of the second bay and see if you have some strange bit of plastic sticking out of the SATA connector?
Good luck with this adventure! Keep us up on how it's going.