did you try to push that little button to do a hard reset of the AE?
If your AE has a different network o==already running on it and your Airport on your Mac is connected to a different network, it obviously won't see it.
If you do a HW reset, you should be able to find the AE default network in teh WIFI settings in menu bar
THen connect to it and set it up to join your other network
Your Mac can connect only to 1 network at a time
Unfortunately, a solid amber light that will not change to blinking is usually a sign that things are not well with the Express.
Try a Factory Default Reset to see if that will unlock the device
Power off the Express for 15-20 minutes
Hold in the reset button and keep holding it for another 7-8 seconds while you simultaneously plug the Express back in to power
Release the reset button after the hold period and allow 40-45 seconds for the Express to display a slow blinking amber light
If you try this 3-4 times and the light stays solid amber, I am afraid that there is an internal power supply problem with the Express and it will need to be replaced.
Solid amber light on the Airport devices indicates that the unit is starting up. If however, the light stays amber that would usually be a hardware issue.
Try leaving the device disconnected for about a minute. Then factory reset the Airport Express. If the lights stays amber, visit your local Apple Retail Store for service options.
My AE usually works fine. But, every once in a while, I get the dreaded solid amber. Here's a handy fix-it guide:
1. If you are doing an initial set up and getting the solid amber, it's possible that my suggestion will help -- it's easy, so try it. But, it's probably something else and you should consider a factory reset and start the setup over.
2. If your AE has been working fine in the past, the status light is solid amber, the AE Utility doesn't see your device, and iTunes can't find it:
Method A, easy for non-techies: power-cycle your router (unplug for 30 seconds, plug back in).
Method B, easy for techies and avoids disurbing the devices that are working properly: open up your router's admin panel, display the DHCP clients, delete the AE entry, wait 5-10 seconds, refresh the DHCP client list. If you see the AE, you're done and everything s/be fine. If not, power-cycle the AE and see if that works. [I've never had to do that last step.]