Whenever the timer at Champion Select runs out, I am met with the first image; a blank screen.

After closing the client and relogging, I have the familiar screen with the orange Reconnect button, as shown. However, when I click it, the game does not go into the loading screen. Rather, it minimizes and everytime I bring it back up, the Reconnecting screen appears again.

I can't play any games, and I've unfortunately left a team in a 4v5 because I cannot join the actual game. I tried entering custom games, but I am met with this issue there also.

I can access the client just fine.

Oh that happened to me too.
You need to repatch. If it doesn't work then repair.
If that doesn't work then reinstall.

Hope it helps.

Hardcore Pwn are you still getting this issue after repairing/reinstalling?

I've had the same problems. Reinstalled and it worked like a diamond.
~Puts on sunglasses

Initially I wasn't even able to launch the client properly, even when I ran it as admin.

I repaired, but it did nothing.

I found a solution on the EUW forums that involved deleting parts of the files, and having it repatch. This fixed the problem of actually launching the client, and now I am faced with this problem.

Edit: I re-repaired it to no avail. I'll try re-installing shortly

Edit2: Re-installed it. Works fine now, but its definitely something that needs fixing.

can you be specific about what parts did u have to delete?