I have an Amana ALE643RBW drum needs manual assistance to tumble

Over the years I've found that if it buzzes but will only start when you "assist"it, the drive motor is at fault. The hot smell you describe backs that up.. This assumes the idler is ok and the belt is routed correctly. Make sure the belt is on the motor pulley and not riding on the motor shaft. This can happen sometimes if you have to install the belt by feel when you can't see it well . That said, the motor should still start without assistance even with an incorrectly installed belt.
Good luck

Could be a broken belt spin the tumbler by hand it if it spins real easy the belt is off or broke another thing to try if you have resistance when turning the drum have a helper for this one open the door and hold the door switch in set timer to a cycle and press start while holding switch and buzzing spin drum and see if it will continue to rotate while holding switch if so motor going bad

A dryer motor has a build in start relay, yours is probably warned out and needs to be replaced.
For further assistant:
www.quickfixappliances.ca

You have a broken centrifugal switch on the motor. The motor needs to be replaced.

it could be the rear drum bearing(if equipped),the rollers that support the drum have dried up and won't turn,bad drum glides(if equipped) or the motors bearings could be tightening up from lack of oil in the bearings,you need to remove the top and front covers to inspect for all these issues

I believe the light and the fact that it is not running are unrelated.
The light may simply have come loose and needs refitted or may need to be replaced. I'll need the model number of the dryer to help you further on this.
For the noise, try this (you may need two people):
1. Open the dryer door and locate the door switch. While pushing the door switch in, have someone else push the start button. 2. You'll hear the noise. Keep pushing both buttons and take your other hand, reach in side and grab one of the drum fins and manually push the drum in a clockwise direction. 3. The drum may take off on its own. BE CAREFUL TO REMOVE TO HAND QUICKLY TO NOT GET BUMPED BY THE FINS AS THEY BEGING TO ROTATE.
If it does not start, the motor needs to be replaced.
If this works, turn the dryer off, close the door and try to start it again just by pushing the start button. If it works, it may have been something obstructing the drum from turning. OR, the motor could be going out. It may continue to start on its own for an unkown period of time, a day, a week, and year. But eventually it will go out and will need replaced.
Replacing the motor is a bit involved, but if you want to attempt it I can walk you through it. I'd need the model number to go any further.
Most dryers, however, have a 5 YEARS warranty on the motor, so you might consider a repairman. Make sure they are Amana certified and there will be no cost to you for the motor. The labor, however, may be up to you and could be expensive.
I'm willing to assist you on whatever you decide.
Best, G

Try this (you may need two people):
1. Open the dryer door and locate the door switch. While pushing the door switch in, have someone else push the start button.
2. You'll hear the noise. Keep pushing both buttons and take your other hand, reach in side and grab one of the drum fins and manually push the drum in a clockwise direction.
3. The drum may take off on its own. BE CAREFUL TO REMOVE TO HAND QUICKLY TO NOT GET BUMPED BY THE FINS AS THEY BEGING TO ROTATE.
If it does not start, the motor needs to be replaced. If it is still under full warranty, simply call a repairman.
If this works, turn the dryer off, close the door and try to start it again just by pushing the start button. If it works, it may have been something obstructing the drum from turning. OR, the motor could be going out. It may continue to start on its own for an unkown period of time, a day, a week, and year. But eventually it will go out and will need replaced.
Replacing the motor is a bit involved, but if you want to attempt it I can walk you through it.
There should be a 5 YEARS warranty on the motor, so you might consider a repairman. Make sure they are Amana certified and there will be no cost to you for the motor. The labor, however, may be up to you and could be expensive.

I'm willing to assist you on whatever you decide.

Best, G

I have the same problem. While I have not fixed it yet, I assume it is a drum roller. Most dryers have two 4 to 5 inch diameter drum rollers which hold up the dryer barrel in the back. These drum rollers are wheels which have rubber on the outside where they touch the drum and a metal hole in their middle. They turn on a metal rod which goes through their middle. As the inside of the wheel turns on the rod, the metal gets eaten away and they squeak. Replacing one or both drum rollers should fix the problem.

there is a big belt inside that turns the drum , your belt maybe slipped off or broke.

Yes, there is a "startup" switch. It's the button you push on the panel (but I'm sure you know about that).

This switch energizes the start winding in the motor -- when the motor gets up to speed, a centrifugal switch in the motor disconnects the power from the start winding and switches to the run winding.

Either the start winding is not getting power or the winding is bad. If "no power" is the problem, it could be the button on the panel or a loose/dirty connection between there and the start winding. Lot of possibilities which need to be explored.

But if you know about pushing the safety switch on the door and spinning the drum by hand to get the motor started, you can probably fix this.