The router getting a 192.168.100.xxx ip sounds like it's "LAN" IP (the one you use to access it) which is set on the router itself, rather than it's "WAN" IP address which is usually shown under the status page of the router (for example on the d-link dir615 status page it'll report the WAN IP address as issued by the Modem/VM DHCP servers*, which is completely different to the one you use to access the router from your LAN).
What's the modem config page saying?
As normally the "ready" light flashing does mean an issue with the connection - but there is a bug in some of the modem firmware (I can't remember which modems it affect) that will lead to the light flashing when there is a working connection.
The chances are, if the guy/girl on the phone has done their job properly they will have tried to access the modem from their end (something they can do if it's getting a working connection), but if they can't see the modem there is a definite problem.
*Something along the lines of 86.x.x.x