TELLS ME TO RECONNECT TO A GAME THT ENDED AN HOUR AGO

Don't bother. They won't update the client as down, but they ought to. Almost no one can even get into the game. Just let it rest for now. Wait until the boards tell you it's safe again.

There is a known issue right now on Riot's end so just be patient until we have more details. You don't need to reinstall yet. If after this is fixed there are still issues, you can explore other options for fixes with Riot Support.