Contact your ISP.
I have Outlook 2016 (same issue in Outlook 2010) and periodically I get issues like this that get sorted out with ISP support. I use BELL but you may use someone else.
Update:
You need to explain this clearly to the ISP support tech, and also make sure you have the e-mail setup to properly DELETE from server for both systems. You don't want his computer to tell the server to delete every e-mail it downloads, and have you doing the same.
I have it setup to wait TWO WEEKS after the e-mail is downloaded. My dad has a main computer and laptop with the same account so that's the same scenario you are in.
He had his laptop working fine, then his desktop had password issues which the ISP tech fixed.
(ANTIVIRUS software can also screw things up. It's easy to check... just DISABLE any AV software before launching Outlook)