This post is here purely to help those who are Googling for a solution to this problem. Everyone else please ignore!
If you have an HP all-in-one 3300-series printer/copier/scanner, and it starts saying “Scanner error power off->power on”, but powering off and on doesn’t help, then you really need this page. Many thanks to all who posted there!
Basically, you power off the printer and unscrew the screw which allows you to remove the small piece of glass to the left of the main scanning glass.
Using some needle-nosed pliers through the opening, grasp the drive belt and use it to move the scanning head across from the right hand side of the scanning area to the left, until it’s right under the opening. At the bottom of the wide slot, there’s a mirror, and it gets fogged up with something.
Shine a good light in there and use dry Q-tips to give the mirror a good clean. Then reassemble everything and turn the printer back on. After a little warm-up, you should get the ‘Ready’ prompt again, and your heart will be filled with joy.
The whole process should only take about 5 mins. There may be other things which cause a ‘scanner error’, but this fixed it for me and, it would appear, for many others.