I ran into this same problem with the LaserJet M401dn. I noticed this issue occured when the printer was hooked up to the PC via USB. I followed HPs steps on trying to fix this problem and needless to say, their steps weren't worth a hill of beans. The printer is working now now via these steps that I'm going to list.
1) Restart the printer with only the power cord being attached. If you're STILL getting the 79 error service, then it is most likely a firmware issue. Luckily for me it wasn't. The printer started right up as it should.
2) If your printer starts right up, attach an Ethernet cable from the printer to your router/switch/DSL or cable modem.
3) Select the Network icon on your printer screen and check to see if your printer has authenticated to the network and lists an IP address. If you're on a home network the IP address will show something like 192.168.x.xx.
4) Once connected to the network you'll run a firmware update. Click on your Settings icon, select LaserJet Update, Check for Updates Now. Continue by selecting the update and download and install.
After the firmware installs, at this point you might be able to get the printer to work by hooking the USB cable back up to the printer. I on the other hand did a couple other steps before hooking the printer back up.
5) I installed all of the Windows Updates (critical), updated Java
6) Uninstalled the HP printer software for the M401dn and restarted the PC
7) THIS STEP IS NOT FOR THOSE THAT AREN'T FAMILIAR WITH EDITING THE REGISTRY. If you have no knowledge of how to edit your registry, then PLEASE DO NOT ATTEMPT this. Have someone with knowledge do this step. I, nor HP can be held responsible for any mistakes that you make with this step. DO AT YOUR OWN RISK. In the registry I searched for Packard and deleted all Keys or entries that had M401 listed. DO NOT DELETE THE KEY IF IT DOESN'T LIST M401, as there are Hewlett-Packard printer drivers that are built into the operating system and they do show up in the registry.
I ran through the registry twice searching for any sign of the printer driver being installed. Restart the computer again.
8) Reinstall the HP LaserJet Pro 400 M401 Printer Series PCL6 Print Driver that is relevant to your PC. (Sorry, I don't know how to deal with Macs.) DON'T download the Full Software and Drivers or the one WITHOUT the installer. Don't use the disc to install the drivers either. Just download the most recent version of the software from HPs website. Install the software and attach the printer when asked to do so. Hopefully you're golden at this point just like I was!
If for some reason this doesn't work for you, I would format your hard drive and reinstall Windows and all of your software. Apparently there is something within the registry or on your computer that is keeping the printer from working. I hope this helps you all out!