When it's in "problem mode" and consistently not behaving correctly, I would disconnect everything from the CPU except the coin door/slam switch connector and one of the displays. Do you get the 5 second delay then? If yes, add the second display and try again. If it still boots, you've got an issue with the CPU/driver board connector or the playfield itself.
You might try this same test when the machine is cold so you know what to expect on the displays when the CPU boots correctly, but it should be the standard 5 second delay before they kick in.
If it won't boot, disconnect the single display you have connected (power off of course) and connect the other to see if the display is causing a boot problem.
If the board won't consistently boot in this limited connector configuration - absent some type of problem with the slam switch - I'd probably resign myself to the fact there is an unknown (and difficult to diagnose) issue with the CPU board. The last thing I'd probably do before deciding on a new board would be the slam switch modification (got nothing to lose at this point, right?). That way you can take that particular connector out of the equation too and truly isolate the CPU to see if it is booting.
If you truly isolate the issue down to "the machine won't boot properly when it's warmed up", you can start selectively hitting some chips with a little freeze spray while it's having problems (I'd do power off, don't go too overboard) and see if cooling any of them down has any positive impact. Good luck, these things can be a bitch.