This is a simple symptom-cause-solution blog entry only. I hope these blogs will help fellow administrators.
The WebLogic admin or managed server is running, but telnetting to it fails, with an error like:
Trying 10.123.123.123...telnet: connect to address 10.123.123.123: Connection refused
You may be using a development/limited license. These restrict WebLogic to accept connections from up to 5 different IP addresses and then stop accepting connections from any other IP.
If you have multiple interfaces on the server, WebLogic may be listening on one of the others. If you do not specify a listen address for a admin or managed server, it will listen on all interfaces.
Replace the dev license with a purchased one, or restart the server to clear the 5 IPs that it accepts connection from.
Change the listen address, or telnet to the correct address.