If you have a CD, it is issued by a bank. The CD is presumed to be valid unless the issuing bank can prove otherwise. Therefore, you have an IOU from a bank that the bank must pay absent proof of payment to your father. The burden is on the bank to prove payment, not on you to prove nonpayment.
One possibility is that the CD matured and was rolled over or cashed out years ago, and that it isn't any good anymore. That would be highly likely in the case of one from 1983.
If you haven't already checked to see if there is any unclaimed property on file in your father's name, you should. Check www.missingmoney.com for his name to see if anything shows up. If the CD matured but he never cashed it, it may eventually have been turned over to the state. Missing Money is a website that collects information from various states' unclaimed property departments. If something shows up, you can figure out from there how to collect it.
Best wishes to you.
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