you are probabley having one of three problems, wrong driver for card, card not setup correctly or not loaded, and /etc/resolv.conf not correct.
open xshell from a menu and type
if you wireless card is listed with wep key then, probabley need to edit /etc/resolv.conf with correct nameserver. if card not listed then, at xshell
if card is already setup will have a file called myiwconfig.
if file does'nt exist then your card isn't set up correctly. If myiwconfig file is there then open a root xshell and do the following
and see if your card is listed. post your results so can provide further help.
as for puppy verses dsl puppy, you will fine puppy easier to use in my opinion. To get puppy to work better will need to create a swap patitition with gparted.