Whirpool Dryer Model # LER8857EQ1 will not heat. Have replaced heater coil, both thermostats, (one had tested bad), still doesn't heat. What else could it be? There's one other piece attached to the top of the metal housing where the heater coil is. Doesn't look bad, but I'm not sure. What is it, and could that be the problem? Some type of relay or capcitor?

You have checked your circuit breaker for both sides to be on right? The motor, lights use one side (110 volt) and the heater uses the other side (110 volt). There is usually a thermal fuse also to be checked which will go if the dryer gets loaded up with too much lint. It is a one time fuse that has to wired back in with a new one. The piece you described could be this fuse. Just check it's continuity.