This could be kinda tough to pinpoint the problem.
Meaning it could be a lot of things.
If it is just the one user.
1. He has connection issues with the internet. It just appears to him it is just your site.
2. His firewall settings may be in play.
3.His browser internet settings may be in play
4. Cookie issue?
I would start with asking what browser and version he is using.
What internet security he is using.
When does it happen.
As far as being a fast computer means nothing for just opening the summary page. Meaning not downloading anything.
Unless you have a lot of high intensive graphics on your main page.
Try using the same browser he is.
Then I would suggest to him to disable not reset all security settings. Browser,firewall bla bla. One at a time.
This could be easier if you were in front of his machine.
PS
the not connected status means the browser could not connect to your page. So either he has a connection issue or your host does.
Could it be he uses a different physical connection to the internet.(laptop on wifi and desktop on hardwire?)
