See this
post for my recommended reading list.
If you didn't enter a root password, just hit enter when it asks for a password.
Once in, enter
passwd to change your password. It's just that simple.
I don't think there's anything wrong with your installation, unless you borked something when you cut the power. The behavior you described sounds normal to me.
If your system returns an error message (invalid password, or whatever) at login, use your boot disk or boot from Slackware CD1. You should be able to figure out how to boot from CD1 by searching this site--or perusing the Slackbook--and then following the onscreen instructions.
If you find you just can't get it sussed, let me know and I'll walk you through it, but I want you to try it on your own first. It'll help you break away from "thinking in Windows" faster than if I hold your hand the whole way (plus, my wife'd object and I just don't like men in that way
).