Well thank you for your faith in me but I'm struggling with this one.
The warning box you're seeing with YouTube is the standard alert that you'll always see when switching from a secure ('https') web page to a non-secure ( = normal, 'http') page, unless (as most people do) you've at some time clicked on 'Do not show this message again'.
I'm rather concerned that secure log-in pages seem to be redirecting you somewhere. It's possible (but by no means certain) that there's something nasty on your PC which is trying to direct you to 'fake' log-in sites, in the hope that you'll reveal personal information (such as bank details). If so, the good news is that the fake sites seem to no longer exist (which is why your browser can't access them).
Which browser are you using? Whatever it is, it might be best to try an alternative. Most people around here (myself included) use Firefox:
http://www.mozilla-europe.org/en/firefox/
Chrome also has quite a few fans:
http://www.google.com/chrome
Also (since there's a possibility of a virus or malware having found its way onto your PC), run a full virus scan and scan your PC with these programs:
Adaware:
http://www.lavasoft.com/products/ad_aware_free .php
Spybot:
http://www.safer-networking.org/en/index.html
I'm sorry that my answer doesn't fully answer your question but I know that people like ChuckFickens and ACtheTroll will also read this thread, so one of them might be able to help further.
Chris