HP Deskjet printer buying guide

I get this error message on my HP’s LCD screen when I boot up the all-in-one printer. It appears to be a problem with the printer itself and not related to my connection to the printer. I can, however, print to the machine without a problem (when the wireless is working). I cannot find any reference to the error on HP.com and tech support was no help. I have tried to turn the printer off and on, and I tried to unplug it for a while to hopefully clear the error. I bought the printer in September shortly after it was released.

When I attempt to print the pictures on my hp psc 750xi printer, they come out looking like a test pattern in colored ink.

I have a HP Photosmart C4580 Wireless Printer. I am unable to install it wirelessly. I have a wireless N Dlink router. I am able to access all the functions of the printer if it is connected to the laptop through the USB drive. But I am not able to install it wirelessly.
Should I fall back to a Wireless G router? I bought the N router thinking that it would be backward compatible for all such day-2-day requirements.

I do not know how to unistall or install a disk so that will need to be explained. I am able to print if I scan an item, but nothing from microsoft works.