The bottom line for all: nothing beats proper troubleshooting. So far I have not see one mention of what the battery voltage was much less use of a proper scan tool.
Without proper information might get better luck on the psychic hot line.

The solenoid is a triage point can either point backwards (battery, electronics) or forward (solenoid, starter) but is the place I would start for nothing when hot (and without a coolant temp we do not know how hot), ok when cools down. The real answer to both is "insufficient data".

Know there are those here who are both experienced and knowledgeable but suspect auto shop is no longer taught in high school. Unfortunately those who are are rapidly ageing out and will not be around for long. Then what ?
YWTK