I've installed the new HP printer driver update but nothing.
Where did you install the drivers from? Software Update and/or HP website?
I followed instructions on HP's site to 'reset' the printing system, which I did, still nothing.
Have you tried calling HP's customer tech support? Read the user manual troubleshooting section? Post on their forums?
HOW can I reinstall my printers back into the system?
Try this:
Disconnect all devices from the computer then do the following:
Boot up from your Snow Leopard Install DVD while holding down the "c" key.
Select the language you wish to use, and then choose "Disk Utility" from the menu bar.
Your HD should appear in a panel on the left hand side of the window which opens. Select it and then click on the "repair disk" button in the right hand section of the window.
Once this process has been completed restart your computer and repair permissions directly from Disk Utility.
Reconnect your printer to your computer (USB) and see if you can add it if it does not already show up.
If you have not already done so, check out the following KB Articles:
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I have exactly the same issue with my imac running Mountain Lion.
You will need to post in the Mountain Lion forums as their troubleshooting is different than Snow Leopards. Before you do, check out the following KB Articles:
OS X Mountain Lion: Troubleshoot a USB printer
OS X Mountain Lion: Troubleshoot an AirPort printer