HP printer 79 service error is not one of those service error codes that require you to contact a technical support agent. It is basically an error with the software of the printer which requires you to update the firmware of the printer or by simply restarting the printer. That is as far as my experience with HP printer goes. This HP printer 79 service error usually shows up when there is miscommunication between the printer spooler services and the printer. It is because a new printer firmware update is available, for the updated printer drivers that you have installed or a quick restart.
To resolve the issue for the HP printer error 79, start by restarting the printer. Restarting the printer may resolve any connectivity issues between the printer and the devices error state. But a simple switch off and on may not always work. To reset any error in the HP printer, turn on the printer (if it is not switched on) and wait until the printer is in idle mode. Now, with the printer switched on unplugged the power cord from the rear of the printer. Wait for a couple of minutes, now reconnect the power cord to the rear of the printer. (ensure that the power cable is directly connected to the wall outlet). The printer will automatically be switched on (if not, press the power button to switch on the printer). Check if you are still getting the HP error 79.
Update the firmware of the printer: if the 79 service error is still persistent then update the firmware of the printer. Go to the HP support website, support.hp.com and enter your printer model number in the search bar. Hit enter and from the software and drivers section, select the latest version of the firmware update for your printer, click download. To install the firmware, follow the onscreen instructions and complete the installation.
There are a few cases where an error may occur due to a corrupted print file job caused by a different computer on the same network. If that is the case, unplug the router for a couple of minutes and restart the printer. Check if the HP 79 service error remains or not, by doing that you are removing all errors possibly caused by the devices connected to it.
Next step is to power on your router back and checks if there are any printing jobs in the queue, if there is, be sure to cancel all printing jobs.
I hope this helped you in resolving HP printer 79 service error and let me know if there is anything I can add or missed. I will be writing more on how to resolve other printer related error codes in the future such as HP printer error code 49.4c02 or 0xc19a0003. Do share and let me me know if you need printer support for any products.