Lots of people reported that network manager doesn't work on Slax 7.0.9 beta and thus makes them some problems connecting to internet. It has been also noticed that installing dhcp package fixed the issue.
I can see that the same problem has been addressed in Slackware current today. From Slackware's changelog:
Switched back to dhcpcd instead of dhclient as the default DHCP client in
the NetworkManager.conf file. Either one will work, but it's probably
better to use dhcpcd by default to avoid a nasty surprise for people who
didn't install the dhcp package since they aren't running a DHCP server.
I'm happy that the fix made its way into official Slackware, which means easier maintenance for me :)