It is possible that your chassis battery can have a dead/weak cell when at rest (it still generates rated voltage) and fail the voltage/current test(s) horribly when you put a load on it.
What is the battery voltage when you crank the engine? It should stay above about 9.5 volts, when cranking, if the battery is fully charged and working properly. If it drops below that, consider having the battery load tested. Auto Zone (and others) will usually do this for you for free if you can get there.
How old is the battery? Is it the correct battery (size) for the application?
Of course, as others have mentioned, cleaning all the connections is the next step if the battery maintains voltage. Look for overheated/fried wires in the starting system.
Chum lee