PYNQ Z1; Done and LD13 are on but it seems like both is stuck

There is a startup script that runs to flash the LEDs. Perhaps you modified this, of for some reason it is not running or has been disabled.
See info here if you want to try and check this:

If you can log in to Jupyter and everything else seems to be working, then I wouldn’t be too concerned about the LEDs not flashing if you don’t see any other issues.

If you have other issues, re-flashing the SD card may be the best option as @marioruiz suggested.

Cathal