Hello again :)
I'm going to get someone else a little more experienced with hardware to take a look here. How old is your computer?
The deal is, here's what might well be happening: when you turn your computer off at the wall, it needs a way to keep ticking over the clock. To do this, inside your computer case, on the motherboard, is a little watch battery which basically keeps the clock alive. However, when this battery starts going flat, your computer will keep forgetting/incorrectly remembering the time, which seems to be what is happening here.
The reason you get security certificate errors is that an example certificate might have a start date of 01/01/2011, and an end date of 01/01/2014. If your computer date is set to 01/01/2001, it believes the certificate is invalid, as current date does not lie between start and end. Then pretty much all website certificates go invalid.
You might then wonder why a clock off by not very much can cause the same effect. Well, the computer has systems in place to prevent the use of a truly invalid certificate. Sometimes when say a certificate expired in 2012, people might incorrectly set their computer clock deliberately to say 2011 to make that certificate valid again. Well, there are systems in place to prevent this (it can be quite a big security risk for various reasons), so certificate errors can result just from the computer knows the clock is wrong, irrespective of by how much it is wrong.
I hope that you find this explanation helpful. I find that most people like to get a rough idea of what's going on. As I said before, I'm going to get somebody else to take a look at this thread now, but what it may come down to is we will check the time set in the BIOS (don't worry, you don't have to understand that yet - but basically, we will try to correct the time from a lower level), and if that doesn't fix the issue, you may well have to open the computer up and replace the battery (again, not yet - we'll give you proper instructions, safety tips, alternatives, etc. etc., before asking you to - this is just to let you know the general plan.)
Richard
