Then I tried to reset the Xbee's by ATRE command followed by ATWR.
I believe that RE is read, not reset.
Then I tried to configure the Xbee's by X-CTU which didn't work either.
If the application written by the people that makes the XBees doesn't work, nothing else is, either.
How did configuring the XBees using X-CTU fail to work?
On the other xbee the associate lamp isn't given any light at all? Have I killed it?
Killed it? Probably not. Bricked it? Probably. They can be unbricked with a bit of patience. Google XBee + brick.
I've tried several combinations with different Arduino's shields and Xbee, and seem to locate the Xbee to be the problem?
Start with getting them configured properly, using X-CTU, and tested using the Range test tab in X-CTU.