I've worked with a number of Kindle Touches.  All were sold as non-working.  All but one were fixed by giving them a good charge, then holding the power button for 30 seconds to force it to completely restart.  There is a similar forced restart procedure for other Kindles, and probably most ereaders in general.  After releasing the power button, just wait.  Don't hit any buttons until it has restarted or for at least 5 minutes.  Make sure that if you are charging via USB to a computer, that you eject it and safely disconnect it from the computer before doing the forced restart.

We tend to just put eReaders to sleep between uses, and rarely if ever restart them.  They need a restart once in a while to keep the software bug free.  Often the bugs show up as very slow behavior, or it acts frozen, or doesn't want to wake up from sleep.  Nearly always these are cured by a forced restart.

However if your screen has horizontal or vertical lines, or areas of destroyed image, this won't help.  That is physical damage to the screen, and the only solution is to replace the Kindle or replace the screen.

Also, problems will happen if the battery gets too low before you try to use it, so keep it regularly charged.

Just the other day, my Dish TV unit froze.  The same thing forced it to restart and in a while it was working again.

Hi Neil - thanks for the tip.  I tried this on my kindle fire hd and it turned off but didn't turn back on, no matter how long I held the power button.  I had to let go and then press it again for it to turn back on, and it didn't solve my problem (apps not working properly, not connecting to wireless properly).  Do you have any other suggestions for me?