Unless the severance was part of the initial contract, something else in the initial contract releases you from the non-solicit, or the company breached to contract somehow, chances are that you are bound by the non-solicit. You'll need to bring to contract to a lawyer for a thorough evaluation.
Hello. I'm sorry to hear that you were terminated from your position - that certainly can be quite stressful. In response to your question: the answer depends upon a few factors, such as: (1) the language of the contract; (2) the reason for your termination, and (3) whether or not the termination was unlawful.
Generally speaking, you are still bound by a non-compete clause and / or a non-solicit clause of a contract. The non-solicitation clause / agreement usually contains language that binds a person "upon termination," or "when the employment ends" -- not based on if the person decides to leave voluntarily or not, or if they receive severance. **IF by some chance, the non-solicitation clause stated that you were promised severance, in exchange for signing the non-solicitation agreement, then you might have a claim that the former employer breached their agreement, thus making that clause void. However, most non-solicits are not written this way (even if you had an employment contract where severance was addressed in another section, then a court could address that section to see if it was breached, but the remaining clauses of the agreement usually remain binding.
Lastly, if you were fired for an unlawful reason -- such as discrimination -- then you could argue that the employer's bad faith / unlawful actions negate their right to enforce the non-solicitation (yet this could be a stretch).
My suggestion would be to focus on what other grounds you might have - if any -- to challenge the failure to pay severance. Was there an employee handbook section that could be interpreted as promising severance for years of service? Could you challenge the "for cause" determination? (Do you have grounds to do so?)
I deal with these issues alot. I hope my answer was helpful. For more information, feel free to click on this link: http://www.sarver-law.com/practice-areas.html