At first it wasn't getting hot enough to dry and I thought the heating element was going bad.
I opened the back and removed the lint trap and it was badly clogged so I cleaned it out.
Then when I hooked it back up, now the end of cycle buzzer sounds every time I push start, regardless of the setting

These driers will do that when the lint builds up like concrete on the inside of the air ducts. The thermal overload has blown open and keeps the dryer from running. You will need a volt/ohm meter to find out which one has blown. These fuses are round with an oval flange that attaches it via screws to the sides of the ducts. They usually have gray wires going to them on Maytag dryers, and when you are tracing the circuits they will wire the fuses in series, so you can follow the wires to find all of the fuses. Also, the sensors get blocked from sensing when the dryer is dirty. Halfway cleaning it will not work because all it takes is one clogged up air passage or dirty sensor. 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 (it has to be scrubbed and washed out), vacuum out motor well and clean exhaust. Mark all wires you unplug so you know where they go. If you leave any dirt in the ducts it will blow another fuse quickly or will not maintain the temperature correctly. This is an easier job than you would think. My sister does hers at least once a year since she has five children and the dryer gets a lot of use. Make sure to clean around all of the sensors, and you can check them with a meter and the chart in one of the manuals, 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