according to your read out it is up and running please read your help files for your network manager.
read this very close. Then realize one thing linpus lite is a very small task oriented linux distro for certain machines. your broadcom card is supported by the kernel but you may need to install the firmware. and I have know Idea how to do this with an operating system that does not have root or sudo or all the stuff linux has. if you want something fast and small that does ten times more puppy lnux is the way to go here is a link that tells you how and why you need the firmware.