Hi everyone, here's the situation. I visited my mother Friday evening. Mom has a desktop PC and connects to the Internet via Ethernet cable running from modem to PC; her current ISP is Time Warner Cable. My sister-in-law left her Toshiba laptop at my mother's house and wanted me to install antivirus software on it. To connect to the Internet with her laptop to download antivirus software, I disconnected the Ethernet cable from mom's PC and connected it to the laptop. This did not work; the laptop would not connect to the Internet. I TURNED off the modem and restarted it with it connected to the laptop. This established an Internet connection for the laptop and I was able to download the software.

Now, when I disconnected the Ethernet cable from the laptop and connected it to the PC, the PC would not connect to the Internet. I turned off the modem and restarted it. Again, the Internet connection was restored, this time for the PC.

I'm wondering why I needed to do the restarts of the modem. I have taken my Compaq laptop to my mother's house and connected via the Ethernet cable; this was with an older modem and a previous ISP and I did not have to restart the modem. And, my son visited me about 2 weeks ago and brought his MacBook computer and I simply connected an Ethernet cable to it so that he could connect to the Internet; no restart of the modem was required. Cable modems have no routing capability, so everything you describe is normal. The first device connected to the modem gets a public IP, different device...different public IP. If the older modem didn't do it, it was probably due to different CMTS (head-end) hardware, on the ISP's side. ROUTERS give additional security because of Network Address Translation (NAT). Most LAN's USE the same addresses, i.e. 192.168.x.y
BTW, DSL modems almost always have a built-in router.Thanks, CC, that all makes sense. The previous modem I mentioned was the one she had with her previous ISP, which was a DSL provider. So, it must have had a built-in router. Some cable providers give you a combined modem/router, mine is a rebadged Netgear. If you see more than one Ethernet socket it's probably a router.Just to make it more complicated:
Some cable modems have an integrated cable modem telephone for VoIP, aka E-MTA (EMBEDDED multimedia terminal adapter).Quote from: Salmon Trout on September 16, 2012, 03:50:32 PM

If you see more than one Ethernet socket it's probably a router.

It only has one Ethernet socket.