This answer should not be considered specific legal advice, nor does it establish an attorney client relationship. This answer really depends on the terms of your non-compete agreement -there may be an argument that you signed it and in return they gave you certain conditions of employment, but remember that most non-compete agreements are designed to be in effect even if you were laid off. If you are predicating your livelihood on whether the agreement applies to your situation, you really would need an attorney to review the entire agreement for you, for there are other issues to consider as well.
You should seek an attorney to review the agreement. In addition, since you are no longer a manager, you may be entitled to overtime benefits for which you have not been paid.