Try changing your net mask to 255.255.0.0 (static WAN on your router.)
... and make sure you do not have Block ICMP Ping activated on your router.
Aside from that you could connect the LAN side of your modem to the LAN side of your router, disable the router's DHCP, statically assign IP address', netmasks, Gateway and DNS on each of your router's clients ... unless you intentionally want them to be behind the second firewall in your router.
The gateway and first DNS setting on your clients would be that of the Modem: 192.168.0.1
OTHER OPTIONS
If your router is compatible check into flashing your firmware with dd-wrt or tomato to convert it into a much better router...
"Turn your $60 router into a $600 router"
www.dd-wrt.com | Unleash Your Router
Tomato Firmware | polarcloud.com
Or if you have a spare PC lying around and you really want a profesional grade Router you can add some NIC cards or a Multi-port NIC card and give the Community Version of pfSense a go:
Download pfSense
pfSense is what I use in an old Dell Latitude D610 laptop as a wireless client / bridge router to a WiFi ISP Modem in a similar setup to yours.
I also have both dd-wrt and Tomato in 2 other routers (Linksys WRT54GL) inline to the Dell running pfSense on top of a 80 port Hewlett Packard ProCurve Switch 4000M in the mix.