humm, ive been having the same problem and have not been able to find a fix for it, i can go online with my wii, Forcast Channel, Wii Shop, Opera Browser all work fine, i have Wii 24 connect on and also standby connection.
I managed to get 2 email addreses registerd one of those being my own email addy, i can send myself an email and it goes through within 1 min, but when i reply to the email i sent my self i never get it on my Wii.
I have also tryed putting my Wii's IP addy into the DMZ in my router and that made no difference, ive also turned off all of the firewall settings in the router and once again it made no difference.
I really hope that their is a fix for this somewhere because i would like to be able to get some email other then the ordinary wii console messages
My wireless router that i have is a Dlink DSL-G604T - latest firmware
If any of you have encounted this problem and have been able to fix it please tell us all how you fixed it