I have an "old" (2005-era) laptop I'm trying to get running with some flavor of Linux. I tried a few versions on it and I always seem to run into trouble. Not knowing if this is just a Linux thing or ...

You must have a short in the plug. Just exactly which plug are you refering to? On the computer? Do you have only one? If you have one that still works you might have to get a hub and only use it. Or ...