I have a comet pinball too, and just finished refurbishing it, so I will try to help you. First of all I'd like to know how technical you are, have you worked on electronics before, do you have experience soldering and do you have a multimeter. Maybe all is not required, but it would help.

The problems as far as I can see are not related, the flippers work in a direct manner, and the ball kicker works via a switch to the main board.

The way the flipper works is with high voltage for the initial flip, and then low voltage to keep the flipper 'up'. this is where the end of stroke switch comes in, it switches from one part of the coil to the other. The most important part is adjusting this switch, to make sure the high voltage is disabled and the low voltage is enabled. If the high voltage stays enabled, the coil would burn. If the 2 parts of the switch make contact, so high to low voltage, the fuse would burn. There are quite a few video's about how to adjust the switch so I suggest you look at these and do the adjustment. If the high voltage doesn't make contact the flipper doesn't work, so this might explain it not working at the moment.

Then there is the pinball kicker continuously activating, there is a switch with a metal lever in the opening of the playfield. This switch is normally activated when the ball is drained and rolls onto the lever pushing down the switch. Try and see if pushing the lever slightly up disables the switch and stops the kicker. The outhole switch is switch 45 which is row 5 (why-grn on connector 1J10-5) and column 6 (gun-blu on connector 1J8-7), pushing this switch would 'short' these 2 wires, and yo could measure these 2 pins if this is the case, if not we will have to look at the solenoid activation side.
If you runs the diagnostics, there is also an option to see which switches are activated (test 3 in the credits display), in a fully working comet with no ball inside, none of them should be activated. If this test is running and a switch is activated it will make a sound and show you the related switch number.

Hope this will help you out a bit, let me know how it goes and I'll try to help you further.

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Try this video to see how the flipper switches work. This is a newer generation pinball and has the yellow capacitors which your machine probably doesn't have, but the switches should be very similar. You see that one is closed and one is open, then when you press the flipper button the first one opens, and the second one closes. You can 'bend' the switches to adjust them, but do so at the 'root' of the switch, not at the end, the metal leafs should be straight, not bent.