re/ Model B+
Your symptoms sound like you are trying to boot an older /boot.
Make sure you have the latest image from raspberrypi.org
Due to the change in LAN/USB controller, new firmware is needed.
If you want to use an existing raspbian installation, the following may be enough (must do this on a regular model A / B before using the card on a B+):
sudo apt-get update
sudo apt-get upgrade
You should back up your SD card before upgrading it, just in case anything goes wonky.
One quick way to check if your B+ is OK is to install the NOOBS network install (must be latest version) on an 8GB card, and let it install Raspbian to itself, and it should work.
http://Mikronauts.com - home of EZasPi, RoboPi, Pi Rtc Dio and Pi Jumper @Mikronauts on Twitter
Advanced Robotics, I/O expansion and prototyping boards for the Raspberry Pi