The only way to check connections is to take the cables off completely and take a brass wire tooth brush or a drill with a brass wire wheel and clean all the areas of connections.... That means ALL connections in the main starter and solenoid nut and bolt areas including the main GROUND black wire areas also........
I have lived in AZ. and I know there is no rust in the southern part of the state, but corrosion can happen and will happen from battery acid and just plain neglect on some people's part.....
A good cleaning won't take long and could save you money in the long run..........
Let us know Mon Amie ~!~!