Disconnect the wire at the braker and test the power DIRECTLY at the breaker if you have not done so.

Check to make sure the breaker is seated properly on the panel. Also you did you try operating the breaker? Square D breakers come pre-tripped from the factory (must be some step in their QA procedure). You need to turn the handle fully off and then back on to reset it.

Yes, this means that your garbage disposal is on the same circuit as the lights. In new kitchen constructions, usually every appliance is on it's own circuit including disposal. It's a bit overkill and requires lots of breakers but would prevent the type of scenario you're seeing.

In addition, I always like to put lights-only on a circuit so that I don't see any dimming when receptacles are used.

I.E. when I power up my HD TV, the lights always dim in the living room. It stink but this is existing wiring and not worth the hassle or re-wiring...

Shade

Are you using the tester properly? The reason I ask is you keep using the word "splice". The pro term is "junctioned". Tell us how you used the tester to determine that there is no power at the breaker. The cable must not be "spliced" into 2 separate directions in the laundry room. The cable won't be switched if you run one path out to the garage and the other to the switch. You need to run the cable directly to the switch and from there out to the garage. No splicing or junction boxes are necessary if I understand your intention correctly.

Also, are you using a 15 amp or 20 amp breaker on the 12-2? If you're using a 20a then you need a 20a rated switch.

Thanks for all the advice. For now, I got rid of the switch. I did use a 20 amp breaker and no, previously it wasn't seated properly. But, I'm happy to say that now there is power in the garage. I learned a lot.