So in test mode... they cycle through each and fire?

Probably want to check the connector between the MPU and the Solenoid driver board (big board to the right of it). That's J4 on each board... that's how the CPU tells the SDB which coil to fire comes over those pins. Then J2 and J5 on the SDB are the harness to the coils.. mainly J5 for playfield stuff.

Is your Alltek jumpered correctly?
Do you have 43VDC at your coil lugs?

I'm not really familar with the delta between test mode and game... but the driver circuit is pretty simple. Data lines from MPU come in on J4 go through a decoder... then to the transistors.. to the J2 or J5 connectors.

Use pinwiki and check the basics.. like your test voltages on the SDB, and read the coil logic stuff.

I would go into switch test and verify every switch works.

If the coils work correctly in coil test (in correct order according to the manual, and no coils fire twice during one cycle) then you know the MPU is able to communicate with the driver board and all the wiring is good between the MPU and driver, and between the driver and playfield.

The switches tell the MPU to fire the coils and also score points. Connector J2 on the MPU has all of the playfield switch lines so that should be checked. Cabinet switches are on J3 and it sounds like those are working OK.

doth is correct. You do not have a coil problem you have a switch problem. I'll bet the switches that do not work are all on the same strobe or return line. You need to look at the playfield switch schematic and identify the in-common wire for the non functioning switches.

Hey I'm 30 minutes away from you and also own a future spa. Small world.

Do you have the manual?

http://mirror2.ipdb.org/files/974/Bally_1979_Future_Spa_Manual.pdf

Are you sure you're in switch test? Can't tell but you may be in adjustments. You want to get into switch test and then refer to the switch matrix section of the manual. If it's a new board this should be easy to fix (since it's probably not the MPU).

Take the ball out, go into switch test, now press every switch and look at the number displayed.

Make sure the switch you pressed matches the number in the manual.

I just purchased a future spa last week so I will be following your progress, good luck

Coil 2 is the knocker down in the cabinet, #7 is the top center bumper, 11 is the target reset. The others all work? Sounds like a loose wire or bad coil(s). Examine those coils. If they look good and operate by hand and they all have 43v on the yellow wire you can manually trigger them by quickly shorting the tap of the transistor on the solenoid board to ground.
According to the schematic they are Q3-knocker, Q10 center bumper, Q1 DT reset.