Basic concept of computer?

Difficult to say. In our modern world, I'd say a computer has to be able to store data, perform calculations, and interface with a human, but that implies storer, calculator, and interfacer, not computer. At the very simplest a computer needs to be able to compute (which, in most definitions, means to be able to perform a calculation).

Is Babbage's difference engine a computer? Yes. So the computer is hundreds of years old.

Is the Antikythera mechanism a computer? Yes. So the computer is two thousand years old.

Could there be something before that which is classed as a computer? Yes.

You see what I mean about it being a fuzzy definition.