Have you tried doing the reverse here, putting your old HD inside and then plugging in your new HD via the USB/Firewire case/adapter? I think you'll find the new HD is working just fine.
You see your new HD is likely a SATA III (6.0 Gb/s) drive. But your system was not designed to support such a fast drive it's I/O being SATA I or II (1.5 Gb/s or 3.0 Gb/s) depending on the firmware level and the controller chip it has. If you research your original HD specs and your new drive you note the SATA speed difference.
Thats not to say your new drive won't work here it's just you'll need to see if it offers a compatibility mode (SATA I/II jumper) and you should also make sure your firmware is up to date. Here's the link to a Apple TN that will help you on that EFI & SMC firmware updates for Intel-based Macs.