I have just bought Pi, and I have no monitor to plug into it, so I thought I would do the DHCP trick. I installed the latest Raspbian wheezy (2013-02-09) on the SD and connected the ethernet cable into the router. But when I plug the power cable in, the light on the router does not go on, and the pi doesn't show up in the address list. What could have I done wrong?
the latest raspbian does DHCP just fine, on the other hand, you might have missed something when creating your SD card. i'd recommend to get any cheap HDMI cable to connect your raspberry to any tv (ask your friends?) and see if it actually boots up.
also, the raspberry has 4 LED lights next to the USB connector, red one is power and the green one next to the read means "sd card access", it's supposed to blink from time to time during the boot. if it does not -- again, check your SD card.
When you plug in your ethernet cable and the Yellow and Green LED lights next to the cable fail to light as expected, here's something to check first:
Log in to your modem and look at the port configuration settings. On my modem, this is found under advanced settings.
Ports can be configured to automatically sense the type of ethernet connection. In my case, the ports I was trying to use were set to 1000 Full Duplex. The Raspberry pi 3 can only do 100 Full Duplex, so the modem never set up an actual physical link on the port for the pi. Further, the Link Active and Link Activity lights never came on on either end of the connection.
I changed the setting to auto and rebooted the pi. The Link Active and Link Activity lights immediately started working and the PI had the internet.