I guess I would double check a few things...
From reading the setup, it appears to be designed correctly..
*Modem flipped to bridged mode
*Your own router set to be the only router, with modem in bridged mode there should be no double NAT'ing or IP range conflicts...
*Router uplinks to switch, and all nodes on the network are plugged into the switch.
So to check things....I'm not familiar with that specific ISP supplied gateway, but double check that it's flipped to pure bridged mode, so that your DLink router does the PPPoE, and your DLink router obtains a public IP address on its WAN interface. If you go to www.whatismyip.com the IP address that you see on that website should be the IP address that you see on the WAN interface of your DLink.
*Check firmware version of the router...I'm not sure if that model is one of the models that had some flakey firmware versions.
*Try setting MTU on that router to 1492...some routers don't do the default "auto" MTU very well.
If you run some ping -t tests to some public sites, are the replies nice and clean?
Interesting, have you tried manually setting up the DIR-655 with your internet details as it should be on your external ip if the modem is in bridged mode.
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