New modem will not work with my Belkin F5D7230-4 router

I would start by re-setting the modem. Disconnect the power for the router and modem. Wait a minute or two. Plug the modem back in first. Wait for the modem to complete communication with your internet service provider. When all communication lights are good on the modem then plug the power into the router. It amy take a few minutes to get all the lights. Hopefully this will allow the DHCP to release from the old router and renew to the new one. Make sure if your internet provider requires any manual configurations that they are properly configured in the new router.

The wan light not comming on tells me that the problem is with your belkin router's settings. I do not have knowlege of this modem but most of the cable/DSL modems today have a router built in. I suggest two things.
1. Make sure your Belkin router's Wan is set to DHCP
2. I have had in the past some routers do not like it when the IP numbering scheme is the same for both routers so we need to change the Belkin. First you will need to change your Belkin's router internal IP to 0.0.0.1 (I am guessing your Motorola is using 192.168.0.1) On most routers this will change your DCHP setting to start at 0.0.0.100 but if is not you will have to change the Start IP to 0.0.0.100.
Sorry I cannot give you a step by step but with your manual in hand you should be able to do it.