It sounds like a relay isn't unlatching somewhere. First thing that I'd try is when the battery is disconnected, spray some WD-40 or contact cleaner into the key switch and cycle it through its range several times to clear out any possible non-contact issues.
If that doesn't do any good, find the fuse / relay panel and pull and reseat everything to make sure it's making good contact. There should be a T190 book in the manual thread that has all the info on location and relay functions.
Doing that is the cheapest and easiest first steps before chucking parts at it.