Company Reneging on a Severance Agreement. Sending me Lesser Amount

I signed a severance agreement with a company. The company responded by wanting to change the amount paid in the agreement and trying to get me to sign a new agreement (which I did not sign, but have evidence of that effort). They, then, sent me the leaser amount even though I did not agree to that. If I cash the check that they sent me, letting them know that I only accept this installment as a proportion of the full amount, but expect to receive the remaining amount, does this count as me accepting the agreement? Does the severance agreement hold, if I accept the money even though it is less than the amount that I agreed to? What are my options here? If I take them to court over breach on contract, can I receive punitive or nominal damages for reneging on a severance package?