I am using verizon DSL and believe they only provide me one IP address. I have five bedrooms which all have internet jet. I used a modem for DSL in and connect it with a swithch box. I aslo plug all room cable ports to the switch box. However I have a problem that the internet constently disconnected. What could be wrong?
It sounds like the modem is bridging to one of the devices at a time and rotating around when it receives a broadcast from another device.
Depending on the modem that you have, you can set it up as your router. You are correct in stating that they only provide you one PUBLIC IP address, but if the router is set up as a router and is doing layer 3 functions such as NAT you can have a public side and a private side of the modem with a LAN handing out 192.168.x.x IP addresses.
Or... just go out and pick up a router that fits your needs (LAN speed, wireless, etc...) instead of dealing with the modem. There are some Verizon modems that are only bridged modems, meaning that they will not act as a router whatsoever (the Westell 6110 is the main one that they send out that is a perma-bridged modem).