The HDD units inside external drives are pretty much the same as any intended for internal mounting. That's why you can do what you are trying to do. Except, of course, it's not working so far.
Maybe a clue here: before you started this you had an optical drive connected plus your only Original HDD. Was the optical drive on SATA2? And now that is where your Alien drive is connected, right? Here's what may be happening: your BIOS is set in its Boot Priority Sequence to try the optical drive first, and then the HDD. BUT what it really is doing is: go to SATA2 first, then to SATA1. Well, with your 2-cable limit you have SATA2 now occupied by Alien Drive, instead of Optical Drive.
Do you have a third SATA port? Try connecting Alien Drive to SATA3, and leave SATA2 empty for now. When you power on, go into BIOS Setup right away and go to where the SATA ports are configured. Do four things:
1. Check that the SATA1 and SATA3 ports are Enabled. You might consider DISabling the SATA2 port for now since it has no device attached. If you do, plan to re-Enable it later when you re-connect your optical drive there.
2. Look at the SATA Port Mode for SATA1 (your Original drive). There are choices like IDE (or PATA) Emulation, AHCI, RAID, etc. Note whatever it is.
3. Now check the SATA Port Mode for SATA3 where the Alien Drive is. In some BIOS's you cannot set the several ports differently - there is one setting for all. So if that is you situation, leave it alone. BUT if you can set SATA3 port's Mode separately, make sure it is the same as SATA1 was.
4. Look elsewhere in your BIOS screens for the Boot Priority Sequence. Since you have no optical drive connected now, make sure it is not in the sequence. Make sure the Alien Drive also is NOT in the sequence. You should have ONLY the Original Drive in there.
Save and Exit, and let the system boot. It should boot from Original Drive. Once you're into Windows, you should be able to see Alien Drive in My Computer if it is working OK.
If you do NOT have a third SATA port to work with, the whole thing becomes a bit shorter. But the key thing is that Boot Priority Sequence. Make sure it uses ONLY the Original Drive, and does NOT try to use Alien Drive.
When you re-install the optical drive later, make sure to Enable its port, and to re-adjust the Boot Priority Sequence so it is back in there, along with Original Drive, but NOT Alien Drive.