A: When you acquire a piece of equipment in the form of a gift, the basis is the lower of fair market value or the basis in the hands of the person making the gift. In most cases, the equipment has been fully depreciated before gifting it away; therefore the basis is zero.
Even though you don't get to re-depreciate the equipment if it is completely depreciated out, you should determine what the original cost of the equipment and accumulated depreciation since the equipment is still considered to be Section 1245 property. Meaning that, when the equipment is sold the amount of depreciation taken by your father would be ordinary income. If sold for more than your father paid for the equipment that portion would be capital gain.