Technically the signage implied an agreement, and allowed you to infer one.
But yes, I think that management could not legally insist on more than the posted price, whether for a lost ticket, or for a particular duration. (Unless the sign included "prices subject to change without notice" or something of the sort.)
As a practical matter, challenge this is going to be a pain. The employees on the spot probably have no authority to vary the price merely because the amount programmed into the register differs from the posted sign. At least they will claim not to have such authority. And they won't release the car without being paid the $80 that they will insist is the proper price. To challenge this, a person would probably have to pay under protest, and then sue for a refund, I would hope in a small claims court. Most people will not go to that trouble for $10, which perhaps the management counts on. Publicity might be more effective.