Here is a diagram of the described network.

I have a Zyxel 623 DSL modem plugged into Fa0/1 on the 7206. Fa0/1 is configured to obtain its IP via DHCP. Fa0/0 on the 7206 is connected via ethernet to the uplink port on the 1900. Plugged into the switch is a Cisco 1700 router and a laptop PC. The 7206 is configured to be a DHCP server for the 172.16.35.0 /24 network configured on Fa0/0 (connected to the switch).
Problem
I have a default route configured on the 7206 to point all traffic out fa0/1 (connected to the DSL modem) but nothing plugged into the switch can pass traffic out to the internet. On the 7206 I can ping out to the internet just fine, but on anything plugged into the switch I can not. there is connectivity between the switch and the 7206 (I can ping loopbacks on the 7206 from the laptop) but no traffic is hitting the internet.
On the 7206 I have a static default route set to forward everything destined for the internet to go out fa0/1. Hosts plugged into the switch are pulling an IP from the 172.16.35.0 /24 range and DNS server addresses from the DHCP service as well. For DNS I am using my ISP's name servers. The default gateway is 172.16.35.1, the IP address of Fa0/0.
Logically speaking, if I initiate a ping request from the 1700 or the laptop the device should hand the request down to the default gateway (the 7206 fa0/0 interface) then the 7206 should forward the request out fa0/1 based on the static route. This is not occurring for some reason. Can someone possibly give me some insight into why this isn't working?