Wireless is a pain in the ass. If you're using an ethernet cable, you have to use Auto DHCP under connect.
Xubuntu automatically detects wired connections and is easier to set up wireless connections, I highly recommend you use it. (Xubuntu has more features and feels like more of an OS than Puppy Linux, plus you can set up things like WINE a hell of a lot easier.)
Also, what are the specs of that laptop? You haven't even told us yet.