All router lights glow constantly, even when no signal is passing through device

I had a Linksys router die suddenly last month. A tech support person was on the phone with me for almost an hour. We tried powering down just about everything possible, and pushing all reset buttons in various places for as long as two minutes. Finally, she said the router had died, and we started to make arrangements for a replacement. (It was under warranty.)

During all of this, all of the router lights were glowing constantly, something which I don't recall happening when the router was operating properly.

Something similar happened to me yesterday when using an Asus router at a friend's flat in Prague. Suddenly, I could not connect to the Internet. I noticed that all lights on the router were glowing (except for the left-hand-most one, which appeared to be a light to indicate power to the router). I disconnected the WLAN wire and also the other Ethernet cables. All lights continued to glow steadily. This was so uncannily similar to my Linksys experience, that I assume this router has also died. (Hitting reset had no effect on the lights, nor did hitting the EZSetup button.)

My basic question is whether one can assume that there are very dire problems when all router lights are glowing, even when only the power is attached without any WLAN cables or Ethernet cables.

(NOTE: It was possible to connect to the Internet directly by inserting the WLAN cable into the computer. At least, it was possible on Sunday. It was *not* possible today! The IP address "yellow ball" never found an address.)

Could you specify which model?

Can you ping the setup page?