Server no longer giving access to sites or databases

The problem is, our company ended up switching to a new ISP for various reasons. We weren't sure it was gonna be a smooth switch, so we kept the old ISP in the meantime. And we were correct to assume that, as nothing has worked right off the bat. I'll get to those details in a moment.

So in the meantime, until we figure out how to transfer everything over to the new ISP, we plugged our original ISP back in.. this is where the weird happens. Our internet works, but our domains do not. We can't access the database or the websites that are located on the server. www.safedig.ca for example doesn't work. Do you know what caused this, and do you know an easy fix? We simply unplugged the telus router, plugged in the shaw router, saw it didn't work, so unplugged shaw and plugged back in telus. We didn't touch anything else, and yet we can't access anything.

Any help would be greatly appreciated!

Marcus