Only able to access HTTPS sites; MAMP Apache Server not able to start

Hope this is the right part of StackOverflow for this question. If there's a better forum for this please let me know.

I'm using Mac OSX 10.10.1. The browser version is irrelevant, as I can cURL or check the behaviour in anything from Firefox to Opera and the result is the same.

The problem is that I can only access SSL secured sites, so not even StackExchange.

After restarting, the behaviour disappears and I can access any site I need to.

The only thing that might be causing the behaviour that I can think of is Skype, as it seems to happen after I login to Skype (we use it in the office). I login to Skype using my Facebook details. No-one else in the office does this and no-one else has the problem, so this might be the issue but I don't know why or how to fix it.

Another clue I have is that I am no longer able to use MAMP - the MySQL Server works, but the Apache Server simply doesn't start without anything to say why. Whether MAMP is running or not has no effect on my main issue.

I don't main Mac - my home computer is Windows - so I'm not overly-familiar with the system, and I can't work out why this could possibly be happening.

Any help or pointers would be amazing.