Avoid stutter when watching Amazon Prime video on Mac Mini 32-bit?

I have a Mac Mini that's a few years old.

I'd like to use it for watching online video, because it's small, we're not using it for anything else, it fits nicely under the TV, and I can connect its video output to the TV. We've got a month's free trial of Amazon Prime Video.

It's 32-bit (Intel Core Duo) so it's running Mac OS X Snow Leopard (version 10.6), which I understand is the most recent version of OS X that it's possible to upgrade it to. It has 1Gb of ram.

I've upgraded Flash and downloaded Silverlight and although APV videos won't play on Chrome, they will play on Firefox. Which is ok.

But when I play them back I get stuttering. :( Sometimes it's ok for a minute or 2 and then we get a little stutter, other times its stuttering every 10 seconds. It seems to stutter mostly when there's a big change in the image and lots happening in the audio - that could be my imagination.

To give video playback the highest priority (the machine is not being used for anything else), I did a renice -20 pid for the Firefox process and for the Silverlight process which it spawned. That didn't seem to help.

I know that the problem is with this machine (rather than with our internet connection or our router) because I've tried watching the videos on my laptop, connected to the internet in the same way, and that works well.

I've rebooted the machine and I've made sure there's only 1 logged-in user.

Can you suggest things I could try in order to make Amazon Prime Video play back without stuttering? Thanks!