OK, from what you say it actually looks like it's going to be something simple! The cycle of the machine seems to be working correctly other than the free movement of the slides, so for the moment let's concentrate on what makes them move or hold.
Cycle the mech (it doesn't matter if it comes up a winner or not), manually hold back ALL the horizontal fingers once the slide lock clicks in, then let the cycle finish with them still held back. It might be possible to simply pull the slides forward by hand without running the mech., hold back the horizontal fingers then release the slides and see if they go back all the way (on some machines it's easy to pull the slides forward by hand, on others no so much, but looking at yours it just might be possible).
This will simulate a full payout of all the slides, as there will be nothing to stop them. Do they all move back all the way and make a payment?
If they do not, the problem has to be the slides themselves. If they don't, then something prior to the slide lock releasing is causing them not to move and we can look for that later.
If, with the fingers held back, the slides don't move all the way backwards, start by removing the slides (you may even find that as you release the bolts on the slide cover plate the slides release). It's not unheard of for the top plate to be too tight and holding the slides from moving.
It would be a good chance to remove the slides for cleaning anyway. They appear to be all the same size, so the order is not critical. Remove any rust and polish the slides but, of course, USE NO OIL! Check all the springs are good, and clean the runway the bottom slide moves on and replace one at a time checking the movement on each as you go. Clean the underside of the top plate and check that there is the smallest of gaps between the top slide and the cover plate,but not enough to make the slides jump about (this is a very small gap).
If the slides DO move back all the way when the fingers are held back, then check just one thing for now and come back to us... When the slide lock is engaged, are all the horizontal fingers free to move, or are they held fast by the slides themselves with the slide lock engaged?
As to the award card and payouts, my guess is that the jackpot finger was cut to stop ANY jackpots from paying out and the patches you have found would have covered all the "7", all the "melons", and the first 2 "Bars". To be honest, they didn't need to be covered, but it would look odd if 3 x bars, 3 x melons and 3 x "7" were losers, which in fact they now are. I'd be interested to know what the patches you found were?