From what you've described, I'd say it has nothing to do with Moodle itself but, rather, what comes before application (ie, Moodle) in the iso model ... that of networking.
To even begin to help with specific instructions one would have to know a couple of things (not shared here) ...
With what service provider does your home network connect?
How many hops away is your home network connection to the Moodle?
traceroute moodlefullyqualfieddomainname
What firewall might exist in front of your destination ... ie, your Moodle site?
Upon what network does Moodle server reside?
Is there any filtering for your home network provided by upstream provider?
The way the theme looks, your browser isn't getting what it needs to render the site.
Have you tried clearing your browser cache at home?
Have you tried constant pings from your home network to the Moodle?
ping fullyqualfieddomainnameofmoodleserver
Can you try this: curl -I http://yourmoodleURL from your home network .... that tells a lot, BTW.
Some of what is shown as a test above one can do with a Mac or linux workstation rather easily from terminal. For Windows, you might have to find some networking testing app and install it.
Given the information shared ... the above are 'guesses' and really fishing.
'spirit of sharing', Ken