Hello,
The issues can be far and wide when it comes to your system. Windows ME is not supported and has not been updated. So your using IE6 that hasnt been patched in over a year could be why. You might not have a critical update that is needed to run the browser efficently on your OS. I would wager to guess that would be the issue cause those websites in question could be heavily coded for IE7 or Firefox and not work well in IE6.
I would update Java, Flash Player and your shockwave. See if that helps.
Cheers,
Mak