OK, basics here....
Are you cocking it before hooking up the air source? If not then do that.
If it's still leaking and the black cupseal (that "rubber" thing you found) may be damaged or the Orings on the valve may be blown or the brass valve retainer screw may be too tight.
If it's not that you're not cocking it before adding air then start with removing the back block, bolt and hammer. Then remove the trigger frame. Loosen the brass valve retaining screw about 1/2 turn if it feels tight. Gas it up while all the stuff is off and see if it still leaks.
If it's still leaking and the screw is loose then degass (DO NOT MISS DOING THIS! ! ! ! ) and remove the front plug and the brass screw. Push out the valve. Examine the cupseal on the stem and also the raised seat on the valve where the cut seal seats. If there's any sign of rust or crud buildup then clean that away. It needs to be smooth. Also replace the two Orings on the valve body. They are the same as tank Orings.
Put it all back together and ensure that the brass valve retainer screw is slightly loose but not sticking down under the body surface. It needs to be loose. Any torque at all WILL give you a leak.
I just thought I'd take a quick peek and then the world went all yellow.....