Hi jradams76
I like the ending of Your post-1: "... game ejects a ball ...". (I may be wrong - but) I believe the problem is just the switch on the Q-Game-Over-Relay --- see HowardR 's JPG in post-12, on the right, near the number 14 - switch (on Q-Relay) has wire-color-red-mingled-with-white - has wire-red-yellow.
The Q-Relay MUST "quit pulling" when You start a new game - so this switch is closed (closed when relay is not pulling - we want the relay non-pulling). May use very fine sandpaper to clean the contact-points --- are the wires soldered-on*** ? . If "No luck": I then would like to troubleshoot using Jumper-Wires --- do You have at least two ? --- well, we can use just simple wires - wind around the bare metal of the Jumper-Wire-End - wind around an solder-lug in the pin --- but Jumper-Wires with gator-clips are recommended.

soldered-on***: Wires in the pin connect from "AA" to "BB" --- well a wire can break-off at "AA (here the Switch on Q-Relay)" --- but this connecting wire could have broken-off at "BB" --- we must have this fact in mind when we investigate on "AA (here switch on Q-Relay)". Greetings Rolf

Hi jradams76
(I may be wrong - but) I believe the problem is just the switch on the Q-Game-Over-Relay or the wire-color-RED+WH leading from the switch - (long wire) - through a Jones-Plug - leading to many switches on the underneathside of the playfield --- means no connection.
Wire-color-RED+WH is the POWER-side-connection of the 24VAC-Circuitry in the pin --- a lot of switches --- to relays current is feeded POWER to coils.
My idea is "when we force connection up to the playfield": You can play. I do have an Surf Champ (it is fully running) - I made the "set permanent Jumper" I ask You to do on Your pin. My Surf Champ nicely runs WITH the permanent jumper (O.K. it is not broken down) - my Surf Champ does not act strange with the set permanent Jumper. Please toggle-off Your pin and unplug the main power cord (Safety Reasons).

See the JPG - I took snippets from two ipdb-pictures: http://www.ipdb.org/showpic.pl?id=2459&picno=46683 and http://www.ipdb.org/showpic.pl?id=2459&picno=46684 . See in my JPG the "lemon green curved line" --- the set permanent Jumper. See on the playfield in Your pin --- a naked wire runs from Rollover-Switch (middle) to the Rollover-Switches to the left - also to the right. THIS BARE wire also is wire-color-RED+WH --- easy to clip-on the end of a Jumper-Wire (You have Your pin toggled off) at this bare wire. Then have the Jumper hang loose - clip-on the other end at the Fuse-Holder 24VAC AS SHOWN in the JPG.

Keep Your hands off --- You have set the permanent jumper - now toggle-on - nothing spectacular should happen --- then press the Replay Buton / start a game (and keep hands off the pin - just watch) - the pin should do a simple start / reset. AFTER the pin has resetted and kicked-out the ball - NOW, YOU: Try the flipper-bats pushing them flipper-buttons - can You play ? Greetings Rolf

0Surf-Champ-Work-28 (resized).jpg