I’m sorry but I don’t think it’s the client’s internet. I’ve just tested it again on my own internet. If I visit the site using my PC then it shows Open Sans as the font. If I visit the website on my laptop (which is a new Microsoft Surface, so not antiquated), then the font shows as something more like Times New Roman. Since they’re on the same internet connection, I don’t believe that this can be causing the font changes.
Please could you take another look? Are you definitely using webfonts?