I think I have a GEM of an old car

Draining the gas was a good idea, but not the other fluids. There's still going to be old stale gas in the lines and fuel pump. It will take a while to work that out and get good gas to the engine. You may have to use a squirt bottle to pour gas down the carburetor to keep the engine running at first. The lack of oil in the engine will promote the formation of rust. Even if it wasn't drained, it will run down from the valve train over time and leave it dry. Old coolant left in won't hurt if it wasn't too old at the time. As the engine runs, combustion gases sneak into the coolant and promotes the formation of acids that can eat away at the heater core and radiator. The corrosion inhibitors in new coolant wears out in about two years. That's why we replace antifreeze every two years. If those additives weren't depleted yet, not running the engine wouldn't have caused more trouble.

The biggest concern is the transmission. If it is an automatic, fluid is going to run out of the clutch packs and expose the fiber plates to air. When they dry out they tend to crumble the next time they're put into service. Even when we rebuild a transmission, we soak the new clutch plates in fresh transmission fluid to give them a chance to become saturated. To not do causes them to be not lubricated when first shifted into gear until the pump has a chance to fill the clutch packs with fluid. The rubber seals in the clutch packs are going to dry out too and become hard and brittle. They do become hard just from age and being hot so many times, but driving the car regularly keeps them lubricated. Typically you can expect the transmission to shift into gear and possibly work okay for a few miles or a few days, but plan on needing to have it rebuilt. Expect to see the rubber seals come out in hard little pieces. Even if they don't crack apart, the grit that flakes off the dried-out clutch plates will chew up those seals and prevent the clutch packs from applying properly.