I personally can't provide any advice, however I know this guy had a similar issue:

http://www.silverball-magic.com/smagic/my-machines-sttng-logs.html

It was bad transistors for him. However the difference is that he was having some switches test bad, while you are not.

Were the cannons trying to fire during the cycles? Optos on STTNG can cause some strange issues, I would start by going into switch test mode and and see if the cannon optos are working correctly. if they are, then I would continue to check all optos, starting with the trough.

Also leave it in switch test mode for a couple minutes and see if you have a switch(opto) going off by itself, could be dirty or have an intermittent connection. STTNG is very touchy with optos, if one is failing it can cause many issues.

when was the last time you replaced your cannon wiring loom?
If never; suspect you need a new wireing harness.

My guess is the wiring looms but, it’s strange that they would go out at the same time. Typically the left side goes out first.

Agree with the wiring looms. I had some similar problems and was able to repair the wiring..but a new loom would have been easier.

I too repaired the looms... with solder and heatshrink; but it only lasted a year or two at best in home use. The only "right" way to fix it is with new wire and new crimps or a new harness.

Is the cause of the harnesses going bad simply the mechanical stress of rotating slightly for years / internal fraying of the strands? I don't have a ST:TNG but I wondered about this.

Correct, the wires stress and break internally, the upgraded looms work great.

I had a signal problem with my STTNG and thought it was a defective opto circuit. It turned out that the circuit was operating intermittently, due to a bad pin on the CPU where the molex connector plugs to the board. I cleaned the pin and inspected the connector and it works fine now.

Take the cannon cover off of both cannons. Any loose wires or two things that look to be shorting together?

Also you can go into options and disable both cannons. With this being true can you start a game or cycle problem still exists?

Did you check the mark and home switches under the playfield? I had similar issues with my left cannon and the tab on the home switch was cracked so it did not register every time.

Would be odd for both sides to have a broken switch, but maybe a bad wire since they share a column in the switch matrix.

Good luck.

there is a drop target that will stick from time to time at the top of the playfield. remove the glass and make sure its not sticking.

i had this mystery problem and fixing this fixed my problem. good luck.

Are both the subway diverters working? When the balls are kicked out at the start of a game, where do they end up and are they getting kicked out anywhere?