welcome to pinside.com. "Full House" is a nice looking pin. I do not own one - I own a Shangri-La and a Jolly Roger.
In Switzerland One-Player-Pins are rare - I have never worked on one.
Great, ipdb has a Schema: http://www.ipdb.org/machine.cgi?id=961 -> 5 MB PDF Schematic Diagram. To have a look at the schema I must make a copy onto my computer: "Right-Handside-Mouseclick" -> Save Target as -> then looking at my copy on my computer.
From left to right there are numbers on the bottom of the schema 1 2 3 ... 20 21 22. Bottom to top the letters A B C D E F G.
From Your post-1 I read "Can play a ball when manually put it to the shooter lane". I assume: After playing that ball it rolls into the Outhole --- nothing happens.
I assume: You start a game -> Reset (of Score-Reels) is done - nothing happens.
To transport the ball over to the Shooter-Lane the "Ball Release Coil" (schema 9-F) should fire.
Lets start at 6-D and look for the connection. (Transformer -> wire-yellow -> a Make-and-Brake-Switch-on Reset-Relay -> wire-brown-yellow-white -> (9-D) a Switch-on-Tilt-Relay connecting with wire-red. Upwards -> Switch-on-Outhole-Relay -> wire-Blue -> the "Ball Count Step Up Unit". Up (through connection "1") -> wire-Blue-Orange -> Score-Motor-Switch-4A -> wire-blue-white -> "Coil Ball-Release (9-G)" -> wire-black -> -> -> to the left to the transformer (the POWER-Side of the transformer). ATTENTION: When the pin is running: ALL (most) COILS are under current ! (Because there are switches that are open: the coil does not fire)
Somewhere in that path - one (2, 3 ..) Switch is not closed / contact-points-on-switch are oxidated / a wire has broken off - we must find.
As Your bumpers work: I assume: "Switch-on-Reset-Relay and Switch-on-Tilt-Relay" are closed.
Please have a look at and report: At the time (when the ball should be transported): Does the Outhole-Relay PULL ? Is its Switch closing ? / contacts clean ? wire-red and wire-blue soldered-on ?
When (at end of Reset-Cycle) the Score-Motor turns: Look at schema 14-B: (The "Index-Wheel is closest to the MOTOR, the "Impulse-Wheel" is far away from the Motor) -> See the text on the Switch-A on Wheel-4 "Pulses Ball Release Coil" ?
Does the Motor turn ? does this switch closes ? Contacts clean ? wire-blue-white soldered-on ? wire-blue-orange soldered-on ?
By now (starting the investigtion) DO NOT BEND the contact-blades on Score-Motor (hard to get at / easy to "faulty-bending").
By now: Have a look at these places and report. We might have to use Jumper-Wires to check for (faulty) connection. Greetings Rolf