[COLOR="DarkRed"]When the dryer cools off a while, it sometimes buzzes when starting it, but it will start again. Is my timer supposed to buzz? Is it bad? Is the motor just overheating?[/COLOR]
All depends what is buzzing.
Does sound like it is the motor as it does try to start (buzzes), cannot and then overheats, trips the motor's internal thermal protect and you have to wait for the motor to cool down and reset the protect

[COLOR="DarkRed"]I tried that trick of holding down the door switch, holding down the start button and turning the drum counter clockwise but the motor doesnt start up.[/COLOR]
Are you sure that the normal rotation is counter clockwise.
Also the motor must be buzzing for this to work.

Try turning the drum by hand. Should turn fairly easily. If not could be the drum is jammed for some reason. You may want to try this on a couple other dryers to get a feel for it.
If it is difficult to turn run your fingers around the back and front of the tub to machine seal. To see if something has jammed between the tub and frame (bra wires are famous for this). Be careful in case the object is something sharp.
If nothing is jammed in there you will have to open it up and find the cause.

Could also be that the motor is jammed solid with lint and this is preventing the Start/Run centrifugal switch from resetting (the unit is trying to start with out the motor's start winding in circuit).

If all OK then the motor is probably on it's last legs.