Help me setup my extended wired Network

As far as whether the "main" AirPort should be set up in Bridge Mode or set up as another router using DHCP and NAT, Apple support will tell you to use the DHCP and NAT settings if you call them, and then ignore the Double NAT notice (some users would call Double NAT an error). Apple's own software tells you that the AirPort should be set up in Bridge Mode when you have another router on your network.

There are upsides and downsides to each approach. We can discuss them if you wish. If Bridge Mode has been working well for you in the past, then I would recommend that you continue with that setting.

It is a shame that Apple has not really updated their 4 year old support document, since the newer 6.x version of AirPort Utility makes the setup that you need easier than you might ever imagine.

I assume that you have tested the Ethernet cables to make sure that they are working correctly.

Since you are working on a new setup, you need reset the Expresses back to default settings and then set them up again.

Let's work with the 2nd Gen AirPort first. With the Express powered on, hold in the reset button on the back of the Express for 7 to 8 seconds, then release and allow a full minute for the Express to restart back to a slow blinking amber light status.

Connect the Ethernet cable to the WAN (circle of dots) port on the Express

Now, we will simply follow the instructions in the Setup Guide that came with the Express. Click the WiFi icon at the top your Mac's screen and look for a listing of new AirPort Base Station. Just below that listing, click directly on AirPort Express.

When you click on AirPort Express, the setup "wizard" will open up and take a few seconds to analyze the network. Then, a screen that looks like the example below will appear, except that you will see a picture of your devices and name of your wireless network.

Type in a name that you want to call the AirPort Express and click Next.

The setup wizard will configure everything for you automatically. Watch the next screen carefully to see that the Express is being setup to extend using Ethernet. This confirms that the wizard has picked up the wired Ethernet connection between the AirPorts and will apply the correct settings to the Express.

After a minute or so, you will see the screen below of Setup Complete, confirming that the Express has been assigned the settings that it needs. Click Done...and you are done. You now have a roaming network configuration. Set up the other Express exactly the same way, except assign a different device name to the product.

When you think about it, assuming that you are starting with a new Express, or you have reset it back to new default settings.......all that you have really done is connect the Express, and assigned a name to the device. The setup "wizard" has done everything else for you.

IF.....you wanted the Express to extend wirelessly, you would follow the same procedure, except you would not connect the Ethernet cable. Then, the wizard will see that you have a wireless connection and it will set up the Express accordingly.

Well, if you have disconnected the switch from the AirPort Extreme, and then tested each port and they are OK.....as I suspect....then you either have a defective switch or a miswired Ethernet cable.

In the type of issue that you have, 90% of the time, it is the wiring that is causing the issue.

So, when each Ethernet port on the AirPort checks out OK, next connect the long Ethernet cable to the AirPort Extreme and test the cable. A good cable tester is almost a necessity. If the long cable tests OK, connect it to the switch and test each port on the switch.

Finally, you did not tell us whether you had a managed or unmanaged type of switch, so if your switch is managed, you will need to check the programming software.