About a month ago I replaced my old WRT-54g with the Asus router. Ever since then I can't get to tcfbank.com or their ip address 22.214.171.124 . I am pretty sure there is some setting I am missing in the router, as it works if I by-pass the router. I also have the problem with multiple machines and multiple browsers on the same network.
I have had this problem with both DD-WRT and Tomato installed - I currently have Tomato on it. I have reset the router to factory/default settings with no improvement.
The router must be doing something but since it is only this one site it must be something unusual.
Depends how much work you want to do. You could try to run wireshark and capture traffic with the router in the path and not. Maybe you get lucky and something will stand out. I suspect the actual traffic stream will be encrypted so if the problem is in the application you won't be able to see it and you will be back to guessing the cause.