If you placed your computer into my hands right now, I'd do this:
First, you have installed OS X onto an external drive, this is what you said?
I'd connect the external drive and boot up from it.
You may need to set up a basic administrative account before going further. (you may have already done this)
I would PASS on setting up any account info with Apple for now.
Can you get to the finder?
If so, are you able to mount the INTERNAL drive on the desktop?
Does it mount? If so...
...Is there anything on it you want to save?
If so, copy that immediately to another drive (could be the external from which you're booted)
Next, open Disk Utility again.
"Aim it" at the internal drive. (Click on the "disk1" line)
Can you erase it?
If so, give it a name that's meaningful to you.
I would also run Disk Utility's "repair disk" on it once or twice, making sure you get "a good report" each time.
Next, download CarbonCopyCloner from here:
http://www.bombich.com/download.html
CCC is FREE to download, and it's FREE to use for the first 30 days.
Now, open CCC.
On the left (the "source") you want your external, bootable drive.
On the right (the "target") you want your internal drive.
CCC also has a preference to clone over the recovery partition as well.
Make sure this option is selected.
You also want to be sure that your clone is a full replacement - CCC should be set to "delete anything that doesn't exist on the source".
Now let CCC do its thing.
When done, quit CCC and open the Startup Disk pane in System Preferences and set the internal drive to be your boot drive.
Now I suggest you power down the Mac -- ALL THE WAY OFF.
Disconnect the external drive and reboot.
What happens?