I am assuming that the new motor came with centrifugal switches.
[COLOR="Blue"]
The centrifical clucth does not kick into start the drum spinning[/COLOR]
There really is not a centrifugal clutch, all it does is activate the switches once the motor gets close to operating speed.
One switch supplies power to the heater, this ensures there is air flow before the heater comes on.
The other switch uses it's Normally Open and Normally Closed contacts.
At rest the Normally Closed set connects in the start and run windings, when close to operating speed, they open and the start winding is disconnected. If left in circuit it would overheat the motor.
The Normally Open contacts close when close to operating speed they are usually wired in parallel with the start switch so that you can release the start switch and the motor keeps running.

Sounds like either the motor is defective or you wired it incorrectly.

I would not hold the motor shaft when it is trying to start. it is very easy to rip your hand apart or break some bones.

[COLOR="Blue"]Could it be the timer?[/COLOR]
There is an outside possibility that the timer contacts for the motor are so pitted/dirty that they are dropping a lot of voltage across them.
If you have 120 to the motor when it is running then that is not the case.