With the PS3 having some, ahem, problems today, you may not be able to play Heavy Rain. Ah well! You may as well kill some time by playing it on...YouTube.
Sony's Scandinavian outlet has posted a series of "interactive" clips on the video site, which allow you to "play" certain sections of the game. You won't be able to perform the more incidental actions, but when it comes to making the big decisions, clicking on the clip will take you to a new clip showing what happens next. Just like the real thing.
The first section of this "demo" is above, but just in case it doesn't work, you can start "playing" at the link below.