Well, I've been messing around with 2.5, 2.5.1 and the just released 2.6, and no matter what I do, when I try to install any of them, I get the same blank screen and the same PHP error from /wp-admin/includes/media.php.
However, I noticed 2.3.3 and earlier didn't have this file, so I decided to try installing it. Voila! It works!
So I was obviously installing it correctly, but there is clearly a serious bug in the code of /wp-admin/includes/media.php (from WordPress 2.5 upwards).
As this file relates to the new admin interface, it explains whey some people are getting blank admin screens after upgrading to 2.5 and later, while other people (like me) simply can't install it in the first place.
I am going to need some very serious convincing that this bug has been fixed before I even consider "upgrading" to a newer WordPress version.