At my business I have set up a network to accommodate both wired and wireless connections. My setup includes a Motorola Surfboard SB6141 cable modem, an Ethernet switch, and two Airport Express routers. I recently had my old switch go bad (it was actually an old wireless router acting as a "dumb" switch), so I replaced it with an actual 5-port Linksys switch. Now I cannot get anything to play nicely.
If I shut everything off and then power up first the modem, then the switch, I have Internet connections on the wired PCs. If I turn on the Airports after that, the main Airport Express won't be given a valid IP by the modem's DHCP server and instead ends up with a 169.254.x.x address.
If I shut everything off and then power up first the modem, then the Airports and the switch with all PCs disconnected, the main Airport Express will grab a proper IP address but will refuse to connect to the Internet even still. Connecting the wired PCs after this results in them self-assigning invalid IP addresses.
The main Airport is in DHCP and NAT mode, while the second Airport is acting as a WiFi extender so it's in Bridge mode. Placing both routers in Bridge mode breaks the Internet connection via WiFi, but it doesn't make sense to me that the first router should work properly in DHCP/NAT mode since the modem is already running a DHCP server, and in my limited understanding it seems to me that this would either create conflict or at least a subnet on my network, which I don't want either. What, if anything, is wrong with my network setup, and how do I correct it?