Some malware have been known to cross or bridge the air gaps. But those are extreme.

To answer the question, I would probably nuke the old computer using DBAN (Darik's Boot and Nuke), with at least 1 full pass. Then I would create partitions or format it fresh.

I would not use a factory reset. I will just use a linux CD/DVD/ISO or even WinXP/7/8.1.

It's not ever going to connect to the internet right? So you don't need any other drivers. You don't even need the anti-virus stuff. The nice thing about ISO files is you can check the SHA256 or MD5 and know the installation media is clean. More or less.