well, I called Apple and the woman was nice on the phoen and checked with her experts, but couldn't fix the problem. She said that the airport firewall was off and implied that the airport sometimes doesn't play well with non-Apple routers. She suggested replacing the D-Link router with a AirPort Extreme Base Station.

My impression is that it's probably best to use router and wireless router from same vendor. In retrospect, I wish I had bought a D-Link wireless router since it's cheaper than the airport express, and probably would have worked more reliably. Buying the AirPort Extreme Base Station to replace a perfectly good ethernet D-Link router is less cost effective.