Wat network ur router on? 192.168.x.x?
Are the on the same network group?
Is ur router having a firewall that does not allow ICMP packets? No pinging or anything like that?
To troublehoot this kinda problem,
1. Bring down ur wireless network adapter and bring up ur eth0. Ping it with other boxes.
2. Do the other way round to again for both eth1 and eth0 again.
3. Also Test on this conditions, use virtual ips for both the network card.
i.e.:
root@richard# ifconfig eth0:1 192.168.x.x.x
If both doesn't ping to that router, its the firewall.
Last piece of advice, divide and conquer, do the thing u are very very confident will work first.
Cheers man.