Basic Networking problem - Win7

I am reasonably knowledgeable (not expert) with computers, but I can’t seem to get a grip on networks, even at a basic level. Here is my problem.
I have connected a simple hardware switch (TP-Link TL-SF10050, 5-way) to my cable modem. With only one computer connected to the switch, all is well. ie that computer is connected to the internet. If I have two computers (one desk-top and one netbook, both using Windows 7) connected to the switch, only the one that is switched on first becomes connected to the internet. The fact that either computer can be connected means that the Ethernet cables are OK and fitted properly. In the case of either computer when connected to the internet, I can read the IP address by holding the cursor over the ‘network map’, and in each case all parts of the addresses are very different. Please, what have I missed.
I am planning to go on to connect the switch to a HomePlug mains unit so as to extend the LAN throughout the house. This seems pretty ambitious if I can’t even get the basic network working!
Thanks

Sorry for the repeat. I thought my first thread was rejected for being too long and so resent this shorter version. Ignore this one..

Regards

Most cable modems do not have a built in router and so modems usually only give out ONE IP address. The first computer you plugged into the switch got that single IP and the modem said "Ok, that's it for my IPs". Switches don't give out IPs (at least not yours) and they simply delegate what the router or modem they are attached to says to do. To fix this, you need to place a router between your modem and your switch or simpler yet, replace your switch with a router.