And the only time you dont have to power cycle anything is when the cable modem is already connected to the ISP, and the "READY" light is on. If the modem is on, you can unplug the router, or computer as much as you want and it will always connect.
But if the cablem modem is turned off and the router is still on, you ABSOLUTLY have to power cycle it, once the modem has fully connected to the ISP.
B.T.W. ALL routers work the same.
Router start-up sequence
A router boots similar to a regular computer as it first performs a power on self test (POST) for the hardware, next loads bootstrap code from ROM, loads the IOS image from Flash into RAM, performs a hardware inventory, and finally the router locates and loads a configuration file. You can reboot a router by using the power switch or the reload command.
The modem ALWAYS has to be the first thing powered up and connected to the ISP, before you power up anything else conected to it. ANY network engineer will tell you that.
[edit on 23-6-2006 by LAES YVAN]