Mark in SFlorida

My first post - I have a 05 suburban. 116,000 miles. Just acquired it and dont know much history. It shifts oddly but firmly. No apparent slip. But it acts like it is in tow/haul mode shifting late like 30 mph out of first gear and does not drop into overdrive. The tow/haul light is NOT on. But it does come on when I push the button on the shift lever. A code came on that said "shift solenoid A stuck on" code 472. I cleared it and it has not come back on but still does same symptom. I assume there is a timer. A mechanic (according to recent records) replaced the solenoid but apparantly that did not solve the problem. Trans oil has been replaced recently and filter too I assume when solenoid was replaced. Car did sit for 1.5 years and I dont know if it was driven at all. I checked the tow/haul wires at base of shifter. All looks good. Any thoughts? I am stuck! Thanks ahead of time, Mark