AA 3634 then UA 3376 at O'Hare
La Crosse → Chicago → St Louis
Timetable, Chicago time
13:50AA 3634 from La Crosse at the gate
11:00UA 3376 to St Louis leaves the gate
21 h 10 apart on the timetable, overnight
UA 3376 leaves 21 h 10 after AA 3634 arrives on the timetable: more than half a day, so not a connection we count.