How to fix League of Legends client only opens after the 2-3 minute mark

Try to play with another account in your PC, with this you can determinate if your client need to be repair or not. If after doind that test the problem persist contact them.

P.S: I remember you that u can still unistall League of legends launcher and install it again.

You should attempt a repair. You can repair the client before you log in.

If this fails you should contact Riot Support by logging into the website with your riot games account and sumbitting a support ticket. Theyw will be able to help you fair better than anyone here.

I suggest using the HexTech Repair Tool available directly from Riot: https://support-leagueoflegends.riotgames.com/hc/en-us/articles/224826367-Automated-Troubleshooting-Hextech-Repair-Tool

It will tell you about known issues, has options for re-applying the latest patch or reinstalling the client altogether, it will adjust your firewall settings appropriately if you let it, and has as some other repair options.

One of the important things the official HexTech repair tool will do is to generate logs for use should you contact Riot support.

Of course, make sure you meet the minimum system requirements for the game (and preferably the recommended ones): https://support-leagueoflegends.riotgames.com/hc/en-us/articles/201752654-Minimum-and-Recommended-System-Requirements

If you're unsure how to find your machine specs, there's a tool for that as well: https://www.pcgamebenchmark.com/league-of-legends-system-requirements

Your firewall settings might be blocking League of Legends from launching. Or improper DNS settings can cause a problem in your internet connectivity.

Close all the process of LoL, then follow the following instructions:

1. Right-click on your Taskbar and click on “Task Manager” from the options.
2. In the taskbar, make sure to end the processes named “LoLLauncher.exe”, “LoLClient.exe” and any other process that has "LoL" or "League of Legends" in its name.
3. After you have ended all the background processes successfully, launch League of Legends again and check if the error is solved.

Source: https://quaries.com/league-of-legends-not-opening/