The screen looks like this:
On my PC, it was easy enough: I clicked the checkbox to say "I confirm that I have read the Terms and Conditions, and that I am 18 years of age or older" then I clicked the "Play" button underneath. However, my friend couldn't see the Play button, so she couldn't get past that screen.
My immediate thought was that her resolution might be too low to fit the whole window onto her screen at once. I'm running at 1280x1024, so I asked what she was using. She said that she'd already looked at the FAQ, and she was using what they recommend. That's good, and it shows initiative, but I asked her to humour me and just tell me the resolution anyway. She was using 1024x768, which is indeed what the website recommends. When she increased the resolution to match my monitor, she didn't like the look of it, but it did allow her to see the relevant button; she then paused the video and restored her previous resolution, so problem solved.
In a situation like this, it helps to be quite arrogant: I think of it as the Rodney McKay approach to troubleshooting. Even though I'd never used this website before, and I hadn't read the documentation, I assumed that I knew more about it than the people who actually made it, and I was right. I'm not sure whether I should feel pride or despair about that.
The snag is that the "Instant Access" workaround only applies per session, so she'll need to repeat this next time she goes to that website. Looking at my screenshot, the "Restricted Content" screen is about 560 pixels high, and when I changed my resolution to 1024x768 I could see it all. However, if I enabled the menu bar (in IE8), the Play button almost disappeared off the bottom; I'm guessing that my friend has a couple of other toolbars displayed, e.g. from Google. If I try to scroll up and down, that only affects the background webpage, not the "popup" window. So, I can only assume that Channel4 are trying to be clever, and failing dismally.
Ah well, I've done my good deed for the day, so I'm off to watch tonight's episode of Dr Who.