There is nothing mentioned in this Apple Support document about an AirPort flashing green four times during a reset.
Resetting an AirPort Base Station or Time Capsule FAQ
I've reset dozens of AirPorts, and have never once seen one flash green four times during the reset process.
To perform a Factory Default Reset on an AirPort Express......
Power off the AirPort Express
Wait a minute
Hold in the reset button first, and keep holding it in for an additional 9-10 seconds while you simultaneously plug the AirPort Express back into power
Release the reset button after the 9-10 second hold period
Allow a full minute for the AirPort Express to restart to a slow, blinking amber light
That's it.
I have a functioning Time Capsule network and am trying to get my Airport Express to join.
Please check the model number of the AirPort Express on the side in the faint print. It will start with a letter "A" followed by four numbers, as in Axxxx. What model number do you see?
Are you still using OS X (10.6.8) as your profile states?