Does anyone know anything about hydraulic pumps?

The trim pump is controlled by solenoids, mounted on the side of the pump bracket. Most likely a faulty solenoid. Press the up button, and test for primary voltage at the solenoid. If you have current, use a jump wire to bypass the solenoid, the pump should run. If you have no primary current, the possibilities could be faulty switch, faulty wiring, or faulty trim limit switch.

Is it a mercruiser?

Some hydraulic systems use gravity to lower the out-drive. That would explain the drive lowering without a problem.

When you try to raise the drive do you hear an electric motor running? The pump runs off the battery, the most likely cause is a bad connection to the battery terminals, most pumps ar run directly to the battery and it is common that the wires were missed when the battery was reconnected after winter storage. I have done this a few times trying to work in the dark under the seats.

If the pump seems to be running and the drive is not lifting then it might be low on hydraulic fluid, this is another easy fix but you might have to be a contortionist to get at the fill cap. Usually located behind the battery on the transom.

Hopefully it is just a loose connection at the battery

Good Luck

Ray