I'm sorry that I haven't chimed in sooner. I was away for 2 days at a pinball show. I see you are making great progress. It seems to me that this game has sat for many years and that some switches need to be cleaned and/or adjusted. It also appears that the rubbers are shot as well. First start with the upper pop bumper leaf switch under the playfield (PF for short). With game off, use a Q tip and rubbing alcohol. Soak a Q tip in the alcohol and run it between the contacts using slight pressure. NEVER use abrasive cleaners, sand paper or files. This will destroy the gold flashing on the contacts. The gap between the contacts should be approx. 1/16 of an inch (2 MM). With game off, you can slightly bend the leaf blades with a long needle nose type pliers if you don't have an adjusting tool, if it needs adjusting. Also on the pop bumper switch assy there is a plastic (spoon) that the tip of the actuator sits into. The tip of the actuator should be centered in the spoon. Sometimes the tip of the actuator ( or skirt) can be worn down and will not close the switch enough to make contact. Fire up the game and test the pop bumper. Let the ball roll thru the A or S lane and see if the weight of the ball fires the pop bumper. If it doesn't, try adjusting the switch a little closer. You don't want them too close, otherwise vibration from the lower pop bumper will cause the upper switch to close unintentionally. If the upper pop is still firing inconsistently, then you may need need to disassemble the pop bumper and clean or replace the skirt and/or the spring undernieth the skirt. The spring might be rusty or dirty. Then do the same for the ball walker switches. I bet this will get the ball walker to start working again. If you hear a humming sound coming from the ball walker, it may be stuck from sitting. Believe it or not, that thing can be disassembled and lubed if needed. The white plastic bushing can also be replaced. You can take it apart by removing the E clips. Lube with white lithium grease and use sparingly. Also check and make sure the ball walker coil is good, not burnt looking or swelled. Make sure the plunger moves freely.
Replace the dry-rotted rubbers, this will help with closing the sling shot switches. You will most likely end up having to clean all the switched in you game. It will help immensely!
Also note that all 3 balls must be in the trough for F2K to go into attract mode. Attract mode is when the insert lamps light in a specific sequence to attract potential players looking at the game. Also when in attract mode, the score display will change from current score to the highest score to date, repeating approx. every 5 seconds. If any balls are trapped in the ball walker maze, F2K will automatically eject those balls and let them drain into the ball trough. When all 3 balls are in the trough, it should start attract mode. If it doesn't, then you need to inspect the trip wires in the trough area where the balls line up under the apron. There are 2 trip wires there that will close the micro switches under the pf, telling the MPU that all 3 balls are ready and accounted for. These trip wires are small and flimsy and can easily be thrown out of adjustment. There are 2 different versions of the F2K ball trough because of issues from the earlier version. Please post a pic or 2 of your trough area and eject mechanism. I'm curious to see which one your game has. Hopefully it's the later improved version.
Do you know that there is a volume adjustment knob by the speaker in the cabinet? Try turning it a few times and see if your sound starts to work.
Flickering score displays can be fixed by re-flowing the solder on the header pins. Look for and pins that look like the solder make be loose around the pins. Turn display upside down, heat the solder just enough to melt it and quickly release the heat. this will help the solder re-bond to the pins.
Good luck bro!