Okay, seems I was not too clear in my explanations.
Let me repeat, hopefully more clear this time:
First let's have a look at the message you get. You get "Blender 2.59 does not support playback". So, we can assume that, you may guess it, that Blender 2.59 does not support playing back animations.
Good to know, but what a pity. Blender 2.49 did support it. Okay, what can we do?
Let's have a look at what the "Play Rendered Animation Ctrl F11" buttons tells us.
It says:

- external.png (7.39 KiB) Viewed 8003 times
Plays back rendered frames/movies using an EXTERNAL player.
Nice. Now we could assume that using an external player will help.
But - which player could we enter into the path field we see in the user preferences page?

- pathtoplayer.png (8.79 KiB) Viewed 8003 times
Wait... why can't we use just Blender 2.49 because this version already had no problems playing files?
So, let's browse to the blender.exe in our Blender 2.49 installation and use this application for playing our animations:

- pathexample.png (6.11 KiB) Viewed 8003 times
Sounds logical that at least we have to tell Blender 2.59 where we installed our old Blender 2.49, no? How should it know it otherwise, because there could be so many debug builds or testing/older/newer versions of Blender, and just guessing which application could be our intended blender.exe would be really dangerous.
I think this should be the complete description now.
~Tach