A poor man's battery load test is to turn on the headlights and note how bright they are and while the lights are on, attempt to start the engine. If the lights dim significantly, two possible causes are the battery or the starter. To see which one is the culprit, leave the lights on for a minute or two, then try again. If the lights are much dimmer after the second attempt, I would fault the battery. If the lights are hanging in there, I would suspect the starter. Using caution, feel the battery cables and connections--if one is really hot, you found the problem.
If the lights do not dim noticably, the starter solenoid is bad OR the solenoid is not getting switch signal.