Tengo un error similar después de intentar desinstalar y volver a instalar.
Para mí, tuve que abrir un indicador de cmd como administrador y ejecutar lxrun /install
Cuando se abrió la tienda de Windows, no había ninguna distribución para elegir, luego encontré este comando lxrun /install y funcionó para mí también.
Obtendrá algo como esto como resultado:
C:\WINDOWS\system32>lxrun /install
Warning: lxrun.exe is only used to configure the legacy Windows Subsystem for Linux distribution.
Distributions can be installed by visiting the Microsoft Store:
https://aka.ms/wslstore
This will install Ubuntu on Windows, distributed by Canonical and licensed under its terms available here:
https://aka.ms/uowterms
Type "y" to continue: y
Downloading from the Microsoft Store... 100%
Extracting filesystem, this will take a few minutes...
Would you like to set the Ubuntu locale to match the Windows locale (en-FI)?
The default locale is en_US.
Type "y" to continue: y
Please create a default UNIX user account. The username does not need to match your Windows username.
For more information visit: https://aka.ms/wslusers
Enter new UNIX username: <you type your login here>
Enter new UNIX password:
Retype new UNIX password:
passwd: password updated successfully
Installation successful!
Documentation is available at: https://aka.ms/wsldocs