Thanks for checking. Let's do some checking on your setup.
Open AirPort Utility, select your AirPort Extreme first, and click Manual Setup at the bottom. Click on Wireless just below the row of icons, and make sure there is a check mark entered next to "Allow this network to be extended". Jot down the exact setting that you see for Wireless Security here as well. Update to save any changes and allow 25-30 seconds for the AirPort Extreme to restart.
Temporarily, move the AirPort Express to the same room as the AirPort Extreme and allow 40-45 seconds for it to power up. Open AirPort Utility, select the Express and click Manual Setup. Click on Wireless below the row of icons. Your settings should look like this:
Wireless Mode = Extend a wireless network
Wireless Network Name = Name of your AirPort Extreme wireless network
Enter check mark next to Allow wireless clients
Wireless Security = Exact same setting as your AirPort Extreme
Wireless Password = Same password as the AirPort Extreme network
Confirm Password
Click Update and allow 40-45 second for the Express to restart. Unplug the Express and locate it for now at a point that is about 1/2 the distance from the AirPort Extreme to the area that needs more wireless coverage. Power it up and wait for the green light.
Then check to make sure that the Express is extending by using the same test earlier in this thread. Check your signal, etc. and please report on your findings.