When I turn on W3 Total Cache all the images in BP Media albums disappear, all that I'm left with is just the title of each uploaded image but no image attached.
As soon as I turn W3 Total Cache off again all the images suddenly appear again.
Can you tell me what I'm doing wrong here?
I already answered this in other support channel you have used.
Anyway, for records I have written this tutorial - http://rtcamp.com/tutorials/using-amazon-cloudfront-cdn-with-w3-total-cache-wordpress-plugin/ - on a BuddyPress-Media demo site.
So it must be some mistake in your w3-total-config. You can check tutorial at above link to verify if you are following all steps properly for w3-total-cache.