This is WAAAAY off topic, but I could use some trouble shooting advice please if anyone has a suggestion.

My Linksys router stopped working.  Bought a new Delkin, connected two computers up to it with "wires". 
I have Internet access, but can't get into Outlook 2002.   Everything works as normal on the other computer (he uses Outlook "Express".)

I wire my machine right to the modem and Outlook works fine.   Once it "works" I can unplug it from the modem and connect it to the router and Outlook still works. 

And then I turn my computer off for the night, and I can't get onto Outlook again without connecting directly to the modem.

Delkin only has help on their website if you cannot connect to the Internet.  The Internet is not an issue!

So - It's not the biggest issue in the world.  Just annoying.  I've been poking around trying to find the reason on the web with no luck...

Can anyone suggest what I should be troubleshooting?

Updating the router's firmware might also be worth a try.

Well, if it does launch, but can't send/receive, I would examine the settings in the security software that you are using (firewall, AV, etc). The router may have its firewall, too.
In this case, I think Outlook is just being blocked from accessing the net, maybe the necessary port is blocked. Try to switch off all security software for a moment and attempt to send/receive then.