So after reading this whole thread (really wish I caught this when it was a new question), here's 99% what's happening:
1) Jack said "as long as the networks are logically the same," which they were not. The router was changed, and the static IPs were changed. Business networks, especially when there's a domain involved, are typically not "plug and play" when changing locations. The very first question should have been "Do you have static IPs from your ISP?" Which was apparently "yes, we do." It happens, lesson learned, *always* consult a IT professional to plan an office move like this, every single network is different and someone needs to properly asses *your* network. A $500 consultation fee for a small network is cheaper than thousands of dollars in lost productivity when something goes wrong.
2) I hate Comcast as much as anyone, but they didn't screw this one up. Their responsibility ends with the ISP termination in the office, the internal network is absolutely not their responsibility to plan or configure. The office had a brand new modem/router and the Comcast tech presumably tested that it was giving internet access successfully. They did their part. It's standard practice for an ISP to give you brand new IP addresses when you move locations unless you specifically request to keep the old ones.
3) What's causing your current problems is DNS and IPv6. You're running an IPv4 and an IPv6 network in tandem, but your core infrastructure is not configured for IPv6. So when a device decides to use IPv6 to do a DNS lookup or connect to domain resources, it's going "I DON'T KNOW WHERE THAT IS!!!" and throwing errors.
DHCP in IPv6 works differently than in IPv4 in that everything is sussed out between the router and the individual device, you don't really have a DHCP server in the traditional sense unless you specifically configure it that way. Odds are your old modem/router didn't support IPv6 out of the box and they swapped it with a new one because you were overdue anyway. Disable IPv6 on the modem/router, shut down *everything*, reboot *everything* in the proper order (modem/router > switches > hosts) and this problem should go away.