How to I stop pages from redirecting, whent he advanced setting that should prevent it does NOT work?

Question

Here is the situation. I have the advanced setting checked to warn me when a sit tries to redirect or reload a page, which is supposed to prevent it from happening. However, it isn't working. A page tried to redirect, and I saw the little banner that said Firefox prevented it, then it happened again immediately, with the same banner, and then the page went ahead and redirected, and I did NOT click to allow it. It was as though the page redirect was tried three times, stopped two, then allowed. There has to be some way to stop this entirely. To be clear, I already have it checked under Advanced/General to "Warn me when websites try to redirect or reload the page." It simply isn't stopping the redirect. Yes, I have antivirus protection, and yes, it works. The page that s reloading is a Sims 3 store page. It's supposed to be a video, on the store site, to watch for points. Most re just that, but today some have sown up that, instead of playing a video, it redirects to some other site. One was a health site, with no video to even view! cookies galore, though, which have now been blocked.
Any help appreciated in preventing this from happening in the future!

Answer 1

All good ideas in general, but nothing new installed that I didn't want, and no unknown or new add-ons, either. Great advice, and nicely detailed, though, which should help others that might have those things causing problems. I have seen that sort, when another family member wasn't careful and had an annoying toolbar installed, that was practically taking over when they were online. Took a bt of doing to get that one out; uninstall was the start, but had to clear out some "stray" registry entries as well.
I did notice that if I do not click to close the little pop up banner, it doesn't redirect. Weird, but it worked. I don't know why closing the message without telling it to allow would have that effect, but it did. Also blocked ll the blasted cookies that were showing up, which is something I track, anyway. I can't stand having this or that site track, even if settings are to accept only from sites I visit. Google is BAD about that sort of thing, and some of the social media sites.
Appreciate the tips, in any case.