Here are your parts, includes a wiring diagram.
Parts for Maytag PYE2300AYW Dryer - AppliancePartsPros.com

Did you check that Neutral to L1 has 120 volts?
This is what runs the motor.

At the top on my list would be the thermal fuse (item 5 in the 05-Heater Parts section)
If you click on a parts picture a new page will open with more info on that part. This may be helpful to you.

Note: If you put the unit mid cycle timed dry and the timer advances then the thermal fuse is OK so then check the door switch and the timer contacts and finally the motor windings.

If the thermal fuse is blown you have to find out why it blew.
Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 10 to 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run on high and the thermostats cannot regulate it so the thermal cut-off blows.

The hi-limit should have regulated the temperature so the fuse did not blow, that is why there is a new one with the thermal cut-off..
Note: That unless there is another problem in the unit the hi-limit should never have to open. It is just a safety device with the fuse being a backup safety device.

Just in case it is not a grounded element.
With all the below the high limit will also have to be replaced.
Check that the belt is OK.
Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean your vent system.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut)

Try the following, print out the wiring diagram as it will help.
Short the meter leads together before you start so you can see if there is any zero offset.
Attach one meter lead to the Neutral on the power cord and leave it there.
Set the timer to mid scale timed dry, door switch closed.
Set your meter to the most sensitive scale.

Check to both sides of the thermal fuse both should be 0 ohms.
Check to "1" on the motor, should be 0 ohms.
Check to "S" purple on the timer, should be a couple ohms (the motor windings)
Check to "M" orange on the timer, also a couple ohms.
Check to "L" (probably black) on the timer, also a couple ohms
Check to L1 on the line cord plug end, also a couple ohms.

The above checks the motor circuit.

OOPS!!!

Your readings up to "S" look OK.
But at this point I screwed up and should have told you that the Push to Start switch must be pushed for the other readings.

Note that the cycling thermostat does not matter as it is not part of the motor starting or run circuit
If the resistance readings are OK double check that you have 120 volts between L1 (black) and Neutral (white)

[COLOR="Blue"] The timer motor doesn't appear to run though I have jumped power to it and I could hear it running with power applied directly.[/COLOR]
I am not sure what you did here.
[COLOR="Blue"]
I also checked by jumping directly from L1-black to orange with no reaction from motor.(extra spade to spade connector)[/COLOR]
This will not start the motor.
The orange is not connected to the motor windings when the motor is at rest.
When at rest purple (connector 2 to B and A) connects in the run and aux (start) windings.
When the motor gets close to operating speed the centrifugal switch activates (connector 3 to 2/B) the aux winding is disconnected and the run winding remains connected.
This is done because if the aux winding is left in circuit the motor will overheat.
[COLOR="Blue"]
... as I recall, white, orange, & purple are the run circuits, green/ground, the other wires are for centrifugal switching of heating elements & timer.[/COLOR]
White is Neutral. On a 3 wire hook up this is also green/earth ground.
Orange is the run winding. It has 2 purposes . First it disconnects the aux (start) winding. Second it provides a parallel circuit path around the push to start switch. This lets you release the push to start and the unit motor keeps running.

The timer is not really switched in by the centrifugal switches.
The centrifugal switch in the lower right of the wiring diagram does switch in the heating element. This ensures that the element does not come on until there is air flow.
In auto modes the timer motor does get power through the heating coil when the coil is shut off so in a way the switch does effect the timer motor.
In timed dry mode the timer motor gets power direct from Neutral through timer contacts (B/TM) to L1.

[COLOR="Blue"]so, what I did by connecting L1 (black on timer) to S (purple) should power the motor and make it run?[/COLOR]
Yes it should have run.

As long as you are sure there is L1 to Neutral power then I would replace the motor.
Just strange that there is not hum/buzz when at least one winding measures OK.

Looks like the motor is around $175.00 so unless the unit is in very good shape I would scrap it.