AirPort Express Not Able to Connect Wirelessly

Question

Hardware is iMac 2.4 GHz Intel Core 2 Duo with 4 GB 667 MHz DDR2 SDRAM.  Mac OS 10.6.8
Connected to Internet via Motorola Surfboard SBG6580 Modem / Router, so I connect by wireless through the modem.
I followed the installation instructions to install AirPort Express to play music on my home stereo.  I connected the Airport Express to the receiver by the tape port.  I was not able to install AirpPort Express via wireless mode, so I connected the iMac to the AirPort Express by CAT-5 hard wire cord.  The installation was successful and the AirpPort Express obtained an AP address.  I was then able to play music from iTunes pm the iMac through the stereo speakers...as long as the AirPort Express was connected by hard wire to the iMac.
When I remove the CAT-5 cord from the AirPort Express, the AirPort Express retains the green light, but it is not able to receive data from the iMac.  To the contrary, the AirPort Utility is not able to find any AirPort wireless devices unless the AirPort Express is connected via the hard wire CAT-5 cord.
As an experiment, I then connected the AirPort Express to the cable modem / router via the hard wire CAT-5 cord.  The AirPort utility on the iMac was still not able to find any AirPort wireless devices.  Further, the model then assigned a different AP address to the iMac so that it was not able to connect to the Internet..
Meanwhile, the AirPort Express still retains the green light, indicating the installation was a success and that it is ready to transmit.
Any advice to resolve this issue would be very much appreciated.  Thanks in advance for your thoughts.

Answer 1

I suggest that you start by performing a "factory default" reset on the 802.11n AirPort Express Base Station (AXn) to get it back to its "out-of-the-box" configuration. By default, the AXn will broadcast an unsecured wireless network with a Network Name of something like: Apple Network NNNNNN
After the reset has completed, plug the AXn into power, and then, verify from the iMac that this network shows up in the list of networks under the AirPort icon in the OS X menu bar. Does it?
If so, then from the AirPort icon, switch your iMac to connect to the AXn's wireless network. Note: You will temporarily lose the Internet connection from your Motorola router. Then, run the AirPort Utility. The Utility should now find the AXn. If not, use the Utility's "Configure Other" option under the File menu option in the Utility's menu bar. Enter 10.0.1.1 for the Address and "public" for the Password.
AirPort Utility > Select the AXn > Manual Setup > AirPort > Wireless
Wireless Mode: Join a wireless network
Network Name: <existing Motorola's wireless network>
Wireless Security: <select the encryption type of the existing wireless network>
Wireless Password: <enter the existing wireless network password>
Verify Password: <re-enter the existing wireless network password>
AirPort Utility > Select the AXn > Manual Setup >Music
Enable AirPlay (checked)
iTunes Speaker Name: <enter desired speaker name>
iTunes Speaker Password: (optional)
Verify Password: (optional)
Click Update to write the new settings to the AX