When you install Slackware, the root account receives a mail message titled 'Welcome to Linux (Slackware 14.2)!', that can be accessed by typing 'mail' at the command line. That message has advice on the setup of networking, including:
If you will be using wireless (or even a wired interface), you might
want to let NetworkManager handle your network connections. This is
a choice during the initial installation, but may also be selected
later by rerunning netconfig, or by setting the startup script
to executable (chmod 755 /etc/rc.d/rc.networkmanager). When Network
Manager is used to handle connections, a nice interface is provided
to scan for wireless access points and make changes to the network
configuration. This interface runs automatically with KDE or Xfce.
In fluxbox, the nm-applet program will need to be launched. Other
window managers lack a system tray to display nm-applet, so for those
you might want to look at wicd in /extra, which also provides a nice
GUI tool for connecting to wireless (or wired) networks. For window
managers that do not provide a tray for running programs, start
"wicd-client" to make changes. With NetworkManager or wicd, it's
a good idea to remove any existing network configuration in
/etc/rc.d/rc.inet1.conf first. This can be done by running netconfig
and setting the machine to use loopback. Then, if you're using
NetworkManager run it a second time and select NetworkManager.
For your connection problem, I suggest to try changing the default DHCP client from dhcpcd to dhclient in /etc/NetworkManager/conf.d/00-dhcp-client.conf, as it has been reported that dhcpcd fails with some hardware.