I recently ran into error 21:13 for an HP Designjet Z5200.
While the HP Documentation goes through diagnostics (page 110) on how to troubleshoot the issue, if the machine is not in a state where you can access the menu from then, you'll need to enter the diagnostic mode when the printer boots up.
Here are instructions on how to entering the diagnostics menu
1. Make sure the printer is switched off with the Power key on the front of the printer and not with the power switch on the back of the printer.
2. Press and hold the Up and OK keys. While holding the Up and OK keys down, press the Power key to turn on the printer, then release it while continuing to hold down the Up and OK keys. Wait until the HP logo appears in the front-panel display, then release all keys.
3. In the Diagnostics menu, select a diagnostic test with the arrow keys and press the OK key to begin the highlighted test.
Upon entering the diagnostics mode, you will need to run the Service Station Diagnostic Test, which is menu option 8.
I ran the Service Station, Primer Motor and Aerosol test as recommended by the service manual and was able to get the Z5200 working again.