Yes, I'm guessing that means it's one of the Ads?
Possibly. The blocking of cookies means that it will block the cookies from the ad domain which will cause strange behaviour.
I'd wager that there is a certain ad in the rotation out there that is not coded very well in terms of setting the cookies and is causing a HTML error that makes the page go weird. Outside of this it may be a very specific ad that only a small number of people are getting which has the same issue regardless of the cookies.
Try unblocking them and browsing for a few minutes and see if it resolves the issue.