Thanks for replying cgwhiz.
That sounds like it's exactly my problem too. I think (hope) we can rule out system requirements as the cause considering the difference between our two computers. I have a quad-core with 4GB RAM.
Besides, even if the system requirements were the problem it would still be a problem, since Maya should not do that when faced with a lot of dynamics and fewer system resources. It should just play through really slowly, not play through with no animation at all.
I've been short on time lately, so I can't make a demo scene where this error happens and post it right now, but I should have time soon. If you want to speed things along a little you could post one cgwhiz!
But if you don't want to, no problem. I'll get to it sometime.