The older Mac won't work for a possible solution.
Regarding your statement "Yes it was purchased new, and I already reformatted it, as it has several shows and movies stored on it.". seems strange that you could not use it for a backup. Maybe you needed to partition it, and one of the empty partitions is where you would/could make the backup to.
Regarding the last "step" you mention above, how do you have access to the internal drive, via the Flash Drive? Also, do you have enough room on the Flash Drive to "place" other files/folders, etc.?
Assuming you can do that, you will still need to Erase, Format, and if necessary, partition the internal drive on the iMac. There is the possibility that if the original drive is still in the iMac, it could be going bad, considering its age (6+ years) and what I suspect is that very little (if any) maintenance was performed on the drive. If you can Erase, Format, and if necessary, partition the drive, you could then install El Capitan on it, re-boot your Mac from that fresh. clean installation of El Capitan, and then "moe/re-install, etc." the stuff you previously copied to the Flash Drive. Regarding the applications, if you have any third party apps (like Office 2011, 1Password, etc.), they will need to be upgraded
first before you can use them with El Capitan. The other thing is that the latest version of El Capitan is 10.11.3. If via your process the version of El Capitan you wind up with is 10.11, 10.11.1, or 10.11.2, you can easily upgrade to it without going to the App Store. Just download the OS 10.11.3 Combo Updater from here:
https://support.apple.com/kb/DL1859?locale=en_US
Just for your information, I needed to update 5
critical applications before I could upgrade from Yosemite (OS 10.10.5) to El Capitan (OS 10.11.1). They were:
1Password
SuperDuper!
Onyx
TechTool Pro
Office 2011
You might be wondering why I started with OS 10.11.1, versus OS 10.11. The primary, initial reason was that the first beta of OS 10.11.1 appeared at the beginning of August, a full 8 weeks before OS 10.11 came out at the end of September. So, I had already planned on waiting until OS 10.11.1 was released (at the end of October). The other important reason is that the update for TechTool Pro (to be compatible with El Capitan) was not released until the first part of October (can't exactly remember when that was).
I still have not figured out how to get Onyx to perform its tasks on either of my external drives. I'll try and look into that some more, but I truly suspect that as long as the internal hard drive is not "bad", you will still need to use Disk Utility to Erase, Format, and if necessary Partition, the drive.