Steam server error preventing me from accessing Steam

[silly_lillie]

Ok, so I've posted a part of this thread already in the TF2 forum, as it first manifested there for me, but ever since it's become a much more major issue regarding Steam as a whole.
I've had this problem since Wednesday night where, in TF2, I was playing on a server and everything seemed fine. Then I lost connection and was subsequently booted from the game. Here is the rest of the backstory from the original post on the TF2 forum.
So I've had this problem all day now where I go to get into a game of casual, but when I do, the game finder shows 52 people in game nearby, with 11000+ worldwide, about 70 or so people nearby searching for games and a couple hundred empty game servers. About 5 seconds later, the in-game and empty game servers numbers for nearby change to 0. I am never able to get into a game. I cannot connect to casual, competitive, MvM or even bloody community servers. This problem only arose earlier today. I've uninstalled and reinstalled both steam and TF2 as well as re-started my WiFi and my laptop several times. I don't live in an area with particularly high ping as most of my games have about 20-ish ping (Luxembourg servers mostly). I also had a problem where steam itself wouldn't start saying 'Steam was unable to connect to the Steam servers' but that was fixed by uninstalling and re-installing. I've been forced to play with bots and, as you can imagine, that isn't the most fun (got 40+ kills on Badwater as engi without the blu team taking me out) Is there a potential fix for this?
Oh, before I forget, I have friends who have been playing the game all day and steamstat says that everything is ok.
Here's where the problem involves Steam. I decided to switch to a new hard drive to see if it would solve anything. This involved me having to transfer all files from my original hard drive to the next, along with a driver installer. This then caused me to waste 2 hours downloading 12GB of drivers that didn't even work, to then having to use another driver installer, taking another hour installing the correct drivers. Then, I had to download Steam. This went all fine and dandy until I had to log in. I entered my password and username in fine and then it said that 'Steam was unable to connect to the Steam servers'. I pressed retry. This came up with the authenticator code screen which I entered, only to be greeted with the same message as before, and after retrying again the authenticator screen again. I completed this process multiple times before giving up. I decided to launch Steam as an administrator which (for some reason worked) and I was able to spend another hour installing TF2. At this point I had to restart my laptop after TF2 had finished downloading as the drivers had finished installing and required a reboot. After that is complete, I go to load up Steam to be greeted with the usual 'Checking for updates' loading bar. Then it disappears. Nothing happens. Steam never loads. I click it multiple times. Nothing. I run it as admin. 'Connecting steam account forine110'. 'There was an error connecting to the steam servers'. And this is where I'm at now. I've tried using both a wired and wireless connection, completely different hard drives, and completely updating all drivers. The thing is, Steam obviously works in browser, as well as mobile, just not the steam app.
I apologise for the long read but I beg of you, please supply me with any help you can give me as not only may this help me, but also other people in the same situation, as I was unable to find anything related to my issue anywhere.