Mac addresses are fixed and unique to each network interface - they're not assigned in the way that an ip address usually is.
If you've got 2 wireless access points, I wonder if one of them is giving out incomplete/wrong information , ie the default gateway address?
If it's a Windows computer, the command ipconfig will tell you what it thinks the default gateway address is, as well as other information about your interface and address.
(Sorry, I'm not familiar with Mac or Linux so don't know the equivalent commands for those).
I did have a similar sort of problem myself a while back, I'm using an old router/modem as a 2nd wireless access point, and found that although the DHCP from the ACTUAL router/modem was correctly being passed through, the address of the default gateway etc wasn't. The result was that the computer requesting an address would be granted a valid address, but had no default gateway set, and so failed to access the internet, yet could ping and be pinged.
Ian