Hi Cannon500.
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Sorry to hear that you are having errors pop up when attempting to print over your network. This sounds like a router issue more than a printer issue. Have you attempted to reset the network? I suggest that you do a complete shut down on all of the computers and all the printers. Once they are all off, leave them off. Disconnect the power cable from the back of your router and let it sit for at least 4-7 min. While the router is off, please make sure that you have the printer power cables connected to wall outlets and NOT connected to Power Bar's/Strip's. HP printers already have a built in surge protector and if you have them plugged in to a bar/strip , the printer (s) will not get all the power needed to function properly and can give false errors on the printer screens or even have connectivity issues. Here is a document that explains the Issues when Connected to an Uninterruptible Power Supply/Power Strip/Surge Protector.
Please follow the steps in order when booting up the network. Plug the power cable back into the router and let it power all the way on. Once it is all the way back on, please power on all of the printers. Once the printers are all the way on, then power up the computers. Always do the computers last so that they can see the router and the printers upon start up.
Hope this resolves the issues.
Always happy to help so please feel free to write back if you have any other questions or concerns.
Thanks for your time.