I had the ink system failure on my HP Photosmart
8250. Here is how I fixed it...no promises that this is the problem with all of these failures:
Start by opening the printer up to expose the ink pump on the left hand side. Remove the left side dark grey trim, then take out the screws to remove the left side panel. You will have to use some force. I slightly damaged the plastic because I was impatient - be careful if you want it to still look nice.
The ink pump is in the bottom left. In my printer, a large gear had fallen off of the pump and was laying in the bottom of the case. I removed the belt drive to the ink pump, then removed the large pulley that the belt went around. This lets you put the gear back on the ink pump. Use a dot of glue on the shaft if you want. Now, replace the large pulley and the belt.
This fixes the problem, but does not clear the error code. To do this
, go to http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?product=443024&lc=en&cc=us&dlc=en&lang=en&cc=us
Click on the link for your operating system, then click on, download, and use the link that says "recomend update to fix long power-on cycle and ink system failures" This clears the ink failure trouble code and lets the printer re-initialize the ink system.
Oh...put the plastic back on if you want to. Otherwise, you can leave it off and watch all the bits and pieces move around in the printer.
Again - this is how I fixed mine. No promises that this is what has caused the others to fail. The HP website says not to use the patch if you can see ink coming out of the printer. This sounds like good advice to me as the initialization process runs the ink pump for about a minute.