Yes, the battery is the first (and easiest) thing to check. Many auto parts stores will test them
Cables and grounds should be checked no matter what the problem is.
The starter is not the easiest thing to test and it is sometimes as expensive as a battery. This is the last resort (and is easy to replace). And, no money/time is wasted checking everything else first.
(
This discussion is about as common as the discussion about water-pump placement and overheating.)At least no one has recommended swapping in an 8v battery.
