If you are not using the Genuine HP toner, newest HP firmware will block the toner and you will not be able to print.
To solve this issue, we can do two things.

  1. Make sure the printer cannot reach internet,
  2. Downgrade the firmware to an older one.

I use the version 002.1924A firmware. I previously downloaded the firmware from other source.
it was an exe file. I extracted the exe and took only the FUL file. We just need this file.

Steps to follow.

  1. Remove the toner, if the inserted one is already blocked. (May be you can skip this step)
  2. Disconnect network cable from printer. Later make sure the printer cannot reach internet.
  3. Do a cold reset from settings.
  4. Connect the USB drive to the front side USB port of the printer (USB Drive should contain only the FUL file. (This part I am not sure though. May be you can have other files there.. 🤷‍♂️ ))
  5. Printer will show options for flash drive. Select update software.
  6. Firmware will start installing. wait a while.
  7. When update finished, you can use the non-genuine toner cartridge. Printer will warn you that the toner is not genuine, but it will not block you from using it.

File: HP_LaserJet_Pro_M329_M429_series_FW_002_1924A