You need to log in as root, as the Slackware installer doesn't provide opportunity to create a user account. Creating an user account is #1 on your list of course
Anyway, log in as root. The password section will not give any feedback when you type, so it will look like it's not responding to your input. But that is just password camouflage. It is taking input.
After login, type >telinit 4< to change runlevel and get your machine going graphical. You can edit /etc/inittab to change the default runlevel.