Have you established a default route through your gateway? Manually it looks something like this, though I usually screw up something when trying to post it:
#route add default gw 192.168.0.1 ath0
You will also need to run dhcp, assuming that your router is acting as a dhcp server.
#dhclient, or dhcpcd, or whatever your dhcp command is.
There is usually a way to tie this all together during boot. On Debian and derivatives, it's in the /etc/network/interfaces file. On slackware, I dunno. Hopefully someone else will chime in with the needed help.