You mention that you checked routing and dns. Good, that’s a start. You also mention that your users are not receiving mail nor is mail going out to customers.
Basically, your exchange server is not communicating with the outside world at all. Did it ever? I would start with all of the basics:
What is the default gateway for the exchange server.
Is there a firewall and if so, will it let mail in and out.
Does your dns server point to your isp dns.