If I signed a Non-Disclosure/Non-Compete Covenant employment contract when I accept the job offer and decided to work somewhere else before my start date, do I still need to comply?
Look to the contract. It probably outlines the terms and conditions of the non-compete agreement.
As a general rule, however, a non-compete agreement is due to the fact that the employee will acquire certain trade secrets and other information during the employment that would supposedly put the employer at an unfair disadvantage if the employee were to leave and start up a business that competes with the former employer's business. That, of course, does not apply if you never started working for the employer.
While the answer above probably is complete, I recommend having an attorney review the agreement.
Good luck to you.
Contracts / Agreements Lawyer
As the previous answer suggests, the purpose of an non-compete covenant is to protect the employer from employees unfairly using the knowledge and contacts they gain during employment.
In the states that enforce non-competes, they are generally required to be limited in scope, duration and geography. The balance between protecting the employers interests and the prevention of allowing an employee to earn a living must be balanced.
It may be possible that you were provided with proprietary information and contacts prior to your start date. If so, these elements could potentially be subject to limitations. You will need to look to the specifics of your contract or have an attorney in your jurisdiction familiar with such matters review the contract if you have concerns.
Employment / Labor Attorney
If you did not start working there, chances are that the agreement is unenforceable, simply because there was no consideration for the agreement you signed. You were not paid presumably at all under the contract, since you never began to actually work. I do recommend that you have an attorney review it for you, just to be certain that you didn't breach any other covenant in the contract, which would allow them to enforce it against you.