Hi @else and welcome to the forum!
With 'old' computers there is a chance that they have a 32-bits processor, which is not supported by the latest versions of Zorin (System Requirements - Zorin Help + 32-bit Version of Zorin OS - Zorin Help). Could you check if it is 32-bits or 64-bits?
(see this thread for more info if that is indeed your problem).
To check which processor your computer has you can try out points 4 or 5 in this list, if you still have access to your Windows OS: 5 Quick Ways to Check if Your PC is 32-bit or 64-bit
Good luck!