Here are the parts
Replacement parts for KENMORE 11064932200 | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%203406659.pdf

The most likely cause of your original problem is the motor overheating. The motor's internal thermal protect is the only device that will shut the unit down, then when the motor cools, the thermal protect resets and the unit can then be started again.

Could be:
1. The drum is binding and placing too much load on the motor. Try turning the drum by hand, it should rotate fairly easily.
2. The centrifugal switch to remove the start winding from the circuit is not opening. Leaving the start winding in circuit will cause the motor to overheat.
Could be the switches contacts are welded together. Could also be that the mechanism that activates the switch is not working but usually if this is the case yuou will not have any heat.
3. Could be the motor is on it's last legs.

Your current problem sounds like it is a power problem. Check that the unit is getting 120 volts between L1 and Neutral.
Try flipping the breaker off/on slowly a couple times, sometimes you can loose half the line without tripping the breaker.

[COLOR="Blue"]When I repeatedly push the start button, it sounds like there is a faint clicking coming from the timer dial. Is that normal?[/COLOR]
Hard to say without being here but I would guess yes.
In timed dry does the timer click and advance.
If yes it is another confirmation that the power is OK as it also uses the same power as the motor.

[COLOR="Blue"]Couldit still be a power issue?[/COLOR]
I have lost access to the wiring diagram but it does sound like the power that runs the motor should be OK. The light uses the same side of the line as the motor.

[COLOR="Blue"]Where should I go from here?so very much![/COLOR]
Check that when you push the door switch that the light goes off.
Check the connections at timer, perhaps when you replaced the motor one of them came loose.
Check other connections in the unit.
Recheck your motor hook up.

If all this fails it may be time to get a meter or a pro as you will have to check circuit paths and the easiest and safest way is to use a meter.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.