AirPort Extreme not working with gigabit switches

Hello. I just replaced an old wireless router with an AirPort Extreme. Immediately upon connection, I got significantly improved wifi speeds, but no wired connectivity through the LAN (with several devices attached through gigabit switches). Here's my connection setup:

TimeWarner cable model > AirPort Extreme (WAN) > NetGear 16-port unmanaged gigabit switch ("Switch 1") > NetGear 8-port unmanaged gigabit switch ("Switch 2"). Most devices are connected to Switch 1. Switch 2 is upstairs, with a few devices connected to it.

AirPort is in bridge mode (router off).

After power-cycling several times, I finally got devices connected through Switch 1 to work over LAN. I couldn't believe what a headache that was; my 5-year wifi router never had trouble "finding" Switch 1. At least that's working now....

Switch 2, however, remains unconnected no matter how many resets/power-cycles I do. Which is to say that devices connected to Switch 2 have no wired/LAN access. The switch and all devices connected to it connected fine to the old router (via Switch 1).

Any ideas on why these switches are not being recognized by the AirPort Extreme?

Thanks!