routing to a computer on a switch behind a router?

Unless you really know what you're doing, you only want one box acting as a NAT gateway and DHCP server on your home network. When most people say "router" in the context of a home network, they're actually talking about something that's acting as a full NAT gateway, not a simple IP router.

I'm sure your Vonage box does NAT and DHCP. Also, it makes sure that your voice traffic gets the priority it needs when forwarding it to your broadband connection (i.e. your cable modem). But the Vonage box can only do that for your voice traffic when it's at the head of your network.

So, for best results, make sure your cable modem and your Linksys router are not serving NAT and DHCP. Have the cable modem simply bridge between Ethernet and cable, and have the Linksys box simply bridge between LAN and WAN.

If the Linksys box doesn't provide a way to turn NAT off, then turn its DHCP server off and stop using its WAN port -- just plug one of its LAN ports into the LAN side of the Vonage box. This allows the Linksys box to still act as a Wi-Fi access point (assuming that's what you're using it for -- if you don't need it, then take it out of the picture), and it acts as an Ethernet switch among its LAN ports.

With any NAT gateway, if you want it to forward incoming connection attempts from the outside world in to some host on your LAN, you'll have to set up port mappings in the NAT gateway to tell it which next-hop IP address and port to forward that kind of connection attempt to. If you set up your network with multiple NATs, then you have to tell each NAT about the next-hop NAT gateway, which is a pain and is one of the reasons you should avoid "double NATting" unless you really know what you're doing and have a good reason to do so.

I know what Vonage says about putting it before the router, but I have set this up before and I simply go with this:

Cable Modem--Linksys Router--Netgear Switch

The Vonage box and PC get plugged into the switch.

If this normal, and simple setup does not work, then you can try it their way, but every one I have done has worked. Only caveat, I usually use a Netgear router/switch combo.