The smaller cable on your newer hard drive is likely a Serial ATA cable (called SATA for short).

As for the HDD not showing up...it may be having hardware problems or the partitions could be unmounted or unrecognizable.

Try right clicking on My Computer, and select "Manage" from the menu.

The computer management console should load. Select "Disk Management" from the menu and there should be a listing showing all the drives in the computer and all their partitions. Check to see if the new drive you added is listed there and post the results here.