No internet when booting from Windows to OS X
It sounds to me more like your Airport Express is acting up (since you mentioned that the Mac works fine with your older LinkSys router.) Check for a firmware update via Airport Utility. 
Additionally, you can force Windows to release the DHCP lease on its IP address by going in to the Windows command prompt and typing 

C:\Users\myusername&gt; ipconfig /release


Just do that before you restart into Mac OS X. I agree with @Buscar that you should try to reinstall the BootCamp drivers (and check Windows Update for any updated drivers.)