Airport Extreme won't connect to ISP until ping ISP router address

I recently added a new MacBook (w/latest 10.5.2 updates) and had a lot of difficulty getting it to connect to our ISP through our AE Base Station that worked just fine with our 2 Macs running 10.4.11.

The AE firmware was upgraded to 7.3.1 and I did a hard reset on the AE and re-entered all the setup information. Created a new network name and new network password so existing keychain entries in the old macs would not be used.

The AE is setup to share a specific ISP supplied IP address with a specific ISP provided router IP address and 2 specific ISP provided DNS IP addresses. It distributes a range of IP addresses using DHCP for our 3 computers, 2 airport connected MacBooks and 1 wired enet connected iMac.

It's also set up to bind specific IP addresses to each computer's MAC address using the airport MAC addresses for the MacBooks and enet MAC address for the iMac. MAC Address Access Control is set to Timed Access but there are no wireless MAC address entries so it should be using the (default) unlimited entry.

When I try to connect to the internet from the older MacBook or iMac (both of which are running 10.4.11) it doesn't connect until I actually ping the ISP router address from a Terminal window. Once I've pinged the ISP router the connections seem to be okay until I sleep or shut down the computer(s), then I have to ping the router again before I can make a connection.

I've not seen this problem with the new MacBook that's running 10.5.2, it gets an internet connection every time.

Any ideas why I need to ping the ISP router from the older (10.4.11) computers before internet connections can be made?

Have I missed some configuration step in the AE?

How can I fix this so I get an internet connection without having to ping the ISP router?