Preventing hotlinking through .htaccess checks the referer if I'm not mistaken. So, somehow the living room computer is sending something different for the referer. When or where it works, do you use the www. in the address and do you also use that on the computer where it doesn't work? Just a guess. You could probably write a little PHP file to show the http referer you send from each computer.
Save as referer.php or something and upload it, then visit it from each location and see whether they are correct, or match what is in the .htaccess file.