Even though you're off subscription, I believe your VAR at the time you left subscription can help you.
If hard drive is working, you could make a backup and try to boot it in another computer with similar hardware.
Does this workaround let you avoid the activation issue?
Depends on the license.
If the hard drive is able to boot, you could start SW and get serial number.
You could also deactivate the license so you can activate again.
If you have serial number, login to my.Solidworks.com and enter serial number in profile.
It will show your VAR. You can contact them to remove activation on old computers.
My understanding (but I can not confirm this) is that the serial number activation is linked to the Hard Disk internal device number (the unique identifying serial number or code number for that physical hard disk). It could also be linked to the mother board.
If the software is put on another hard disk (even in the same computer) I am fairly sure it shows as it was re-installed and you loose the ability to have the 2 seats.
I believe (but again am not sure) if you put the hard disk in a different computer it may work if the computer is similar and running the same OS.
It is possible that any re-install of any type or hardware change of mother board will kill your ability to run the 2 seats.
If you try to remove and reinstall on the same hard disk I believe it will also look like a new installation and you will again loose the ability for 2 seats.
It may also depend on what version you are running.
I would first do as Glenn Schroeder suggests and see if they can give you a better answer.
If they can't or won't, I think you are just going to have to take the chance.
Let us know what you try and if it works or not.