Back Online!! A curious tale of computer woes

Two weeks ago, I was happily working with my website, adding blogs, tweaking it here and there. Then suddenly, nothing. A white page that led nowhere.
Possibilities? Well, I am clinging to my trusty laptop even though it is woefully outdated, but another PC and a Mac gave me the same results. Nada. At this point I need to point out we'd had a hard rain the day before and the internet was out or at least intermittent for a couple of days, resulting in a call to the internet provider and a service truck in the neighborhood.
Still, no web page.
But I could pull up any other site on my computer. Seriously. I could pull up any research site, my facebook page, Amazon- quite literally any website except my webpage.. A glitch with my web host? It sounded likely.
One week later, the incredibly nice and helpful support people at Weebly had exhausted their suggestions, and quite possibly a few they hadn't thought of before. Here's where it gets even more curious.
Anyone else could access my webpage. And so could I- from any other internet source.. Using my computer.
Ah, now it sounded like an issue with the internet at my house.
So I spent an hour and a half with a technician with my internet provider delving into the mysterious workings of my modem, computer and website host. He consulted his superiors- three times. The next day a technician came to my house in an attempt to locate the problem. No luck.
In the end, they replaced my modem- instant success!. No one seems to know why three computers at my house could not access my web page, but could bring up any other site.. But the problem has been solved and everything is peachy, now. Any ideas?
Oh, that reminds me to head to the farmers' market for peaches...
Let me know what you think!