1993 Honda Civic brake problem

The car is a 4 door sedan e/w non ABS brakes with 225k on the odomoter. New pads and shoes were recently installed. Brake fluid level does not drop in reservoir.
The brakes are spongy even after bleeding them 2 times. With the engine off, I pump the brakes about 3 times anf the pedal becomes stiff and will hold that way. Once I start the engine, the brake pedal will drop about 2 inches.
If I slowly depress the brake pedal when driving at a speed of about 20 mph, the pedal will go to the floor with very little braking taking place.
At the same speed if I depress the brake pedal briskly, the pedal will go down about half way and the brakes will hold. If I keep pressure on the pedal, it will not drop further.
Any suggestions of what to do would be appreciated.
Thanks,

Mike