What do you mean by the file picker menu doesn't allow me to select a local file to upload - Is the system hanged during that time? If yes, could you please verify the CPU usage during the issue. It might be due to high CPU usage on your system.
Which version of AEM are you using? Also, check in the developer's console if you see any error when you weren't able to select file. Please mention the error trace, it will help in the investigation. Also check error log if there is any error.
Maybe if you aren't on the latest version of AEM, move to the latest version of AEM and try with a different browser.