Second try, just deleted dissertation.
The internal DIR-655 host ping utility probably won't work to public IP. The device is a home router and doesn't support routes to the internal interfaces (LAN).
You set it up as a Bridge/AP/Switch Just make sure you put the right gateway address on your nodes and you should make it to the next hop or Internet.
Your second problem of not finding the SSID is a bit scary. You mentioned it is set to visible is it also set to enabled? Is the router set for the right technology of the handhelds and notebook (b,g, or n)?