Unfortunately, there are no shortcuts here as far as troubleshooting an extended network, especially with a network as complex as yours.
Before we begin the troubleshooting process, can you clarify whether each of the AirPort Extremes are connected back to the Time Capsule using wired Ethernet cable connections.....or....do the AirPort Extremes connect using only wireless?
Or, maybe some of the AirPort Extremes connect to the Time Capsule using Ethernet cable connections and some of the AirPort Extremes connect using wireless?
The first order of business is to make sure that the Time Capsule is operating correctly.
Power off all of the AirPort Extremes and restart the Time Capsule. You want to test with only the Time Capsule at this point. The other AirPorts will remain powered off.
Move your laptop and other portable devices like iPhones and iPads to the same room or to close proximity with the Time Capsule. Check from time to time over the next 3-4 hours to verify that each device has remain connected to the Time Capsule and to the Internet.
If all is well, power up only one of the AirPort Extremes and move your laptop or other portable devices close to the AirPort Extreme so they will pick up the signal from the AirPort Extreme and not the Time Capsule.
Keep an eye on things for a few hours to make sure that things are working correctly.
If they are, power up one more AirPort Extreme. At this point, you will have the Time Capsule and two AirPort Extremes working. Move portable devices close to the AirPort Extreme that you have just powered up so they will connect to the AirPort Extreme and check things from time to time over the new few hours.
You get the idea, power up the other two AirPort Extremes one at a time the same way and check the third AirPort Extreme and finally the fourth AirPort Extreme if the third is operating correctly.
Post back on your progress and we will continue.
