If you want to manually work the top, you have to release the struts. Remove the back seat and interior quarter panels to gain access to the struts (you might be able to do this with the quarter panels in place but removing them makes things easier). You'll see where the shaft connects to the top irons. Release them and you'll be able to put the top up and down manually. As for the hydraulics, you should first remove the reservoir on the bottom of the top pump. Originally, the factory filled these with brake fluid. I would recommend purging any fluid in the system and replacing it with ATF. There are fluid level markings on the side of the canister, when you are ready to "test" the unit, fill the canister to the first level.
I would recommend removing the top motor, etc. disassembling it and checking everything. the motor is a standard starter motor. The valve body that controls the up and down motion of the top, should be cleaned and inspected for pitting. All the internal parts for the pump (valve body) are available however, if the body is pitted inside, the pump may not hold prime. I had this problem with our '47 Convertible and, because I'm not hell bent on restoring it "as Henry Built it", I installed a late model Mustang top motor under the back seat. (the car is 12 volts) and I put a toggle switch under the dash.