D-Link router not working properly

For 3 years I've been using a D-Link router with 3 desktops attached, DSL broadband. No problems. Suddenly, a week ago, I found I could not send email out of Outlook and, similarly, could not get in to sites requiring a password, including my bank, Fidelity Investments, and eBay (I can get to their respective home pages and navigate around to non-password protected pages; I can go to this FixYa website).
Meanwhile, if I bypass the router and hook my computer directly to the internet via the DSL modem, everything works fine.
That would seem to suggest a router problem. But I have tried switching out parts from other systems that are functioning properly. My office has one computer connected to DSL via an identical D-link router. I've replaced that office D-link in to my home system and no go. I've even replaced out my DSL modem and D-link power supply, with no change. I've tried the reset button on the back of the D-link and found that I just have to reconfigure the router (as with an initial install), but no change.
I have not made any changes in my system that I'm aware of and that might of caused a change. I've looked all through properties in my LAN connection and can't find anything out of order.
I'm out of ideas!