So much for that theory that the no start is correlated . I wa s hoping it was a poor connection in the ignition switch.
I removed the key, reinserted, wiggled the key... Nothing.SUre seems like an intermittent connection somewhere. My first guess is in the ignition switch. Next time it fails, remove the key and reinsert. wiggle it around a bit while trying to crank. see if you can get that connection to......connect. Entirely possible the switch connections have a little carbon build up or have worn some.
You could go overboard and remove the column trim and tap it gently with a hammer while they key is in ACC with no chimes. Do some more testing to see if the chimes and no start are correlated.
Could also be loose connection in the fuse box. Had that happen to me once. Maddening.