The fact it would not restore the system image to a single 250 GB HDD could be for either or both reasons. In terms of size, good software might recognize that the contents of the 1 TB drive could fit on 250 GB; however, some imaging software does just that - it creates and wants to restore a complete image of the entire original drive. On the other hand, since there was no second drive to which the image of the 80 GB unit could be restored, the software would have been quite correct to realize that restoring only ONE of two HDD's would NOT restore the system and would not work.
If I understand correctly, you have a Win 10 Pro Install disk. Or, is it an UPGRADE disk that must be run from within a Windows 8.1 that is running? You see, the dilemma is that IF you must have Win 8.1 running, that means you MUST have both HDD's in place and the upgrade will preserve the current structure: the System Reserved Partition on the 80 GB unit will still be there and NECESSARY for your machine to operate. If that is your case, you would be better to do the change I suggested FIRST. That is, you disconnect the 80 GB unit and use the older Win 8.1 Install CD to place the required backups on the 1 TB unit. THEN you upgrade to Win 10 Pro. THEN you reconnect the 80 GB unit, wipe it clean and re-Initialize it.
On the other hand, if what you have is a Win 10 Pro Install disk intended for use with a new HDD, then yes, you can Install it to the 1 TB HDD. If you do that, do NOT connect the 80 GB unit until the Install is complete and working.
HOWEVER, it's not quite "simple". If you do a fresh Install of Win 10 Pro, it will know NOTHING about all your application software - for examples, MS Office, a browser, games, graphics software, Adobe Reader, utilities, etc. A new Install of Win 10 will have a set of Registry files with no information about those apps, and merely copying them from your backup on another drive will not get them working. The all will have to be re-Installed under Win 10 so that they can place the proper info in the new Win 10 Pro Registry. This is one major reason why an upgrade that preserves all your old apps and their Registry entries is much easier than a fresh Install.
So, if your Win 10 Pro disk allows you to UPGRADE, and not just to do a fresh Install, I'd suggest that is easier. As I said, BEFORE you do that I suggest you fix the original issue of having to keep the 80 GB unit installed with its backup files. If you then upgrade with the 80 GB unit still disconnected, the resulting Win 10 will be able to boot properly from only the 1 TB unit, whether or not the 80 GB unit is connected.