My amana electric dryer has been taking a long time to dry and it just quit in the middle of a cycle. When I push the start button it does nothing model NED5240TQ0

These driers will do that when the lint builds up like concrete on the inside of the air ducts. Halfway doing it will not work. You need to totally tear it down and scrape out and wash all of the parts except the motor, which you vacuum out. You can go to YouTube to see videos on how to take it apart, but do a very good job or it will fail again quickly. I would get a new belt and change it while you have it apart and get some white lithium grease and grease any bearings you find. You need to clean out a drier every two years, at least, according to the manual. You just unplug the wires from the sensors and remove ductwork that they are attached on and clean the entire thing with soap and water. Make sure you go all through the dryer and get all parts like the blower fan and housing, vacuum out motor well and clean exhaust. Mark all wires you unplug so you know where they go. This is an easier job than you would think. Make sure to clean around all of the sensors, too. See: Dryer vent cleaning prevents fires - YouTube and: Cleaning out a dryer with top lint cleanout - YouTube
Cleaning out a dryer: By a woman 2 of 2 - YouTube
Here is a manual: https://dl.dropbox.com/u/8010163/Amana_dryer.pdf