I know you said you would prefer Slackware... But you might want to try this at the cost of a disc or two..
Try Fedora Core 2 or 3 as these have a media tester before install, if it works fine then you can rule out your burning of iso's... cancel install, and go back to Slackware
As for linuxiso.org, I have got ALL my distros from their site and I have never had a problem, so I would say you can trust them...
Good Luck and I hope you join the community soon