Put a voltmeter on the battery (should read about 12.6 volts just sitting there). Have someone try cranking it while you watch the meter. If the voltage dips below 9 volts the battery is either going bad or not being charged properly by the charging system. If it stays above 9 volts and everything goes nuts then you still have problems elsewhere.
The SJB is easy to check for water incursion, just look around for moisture in the area of the passenger kick panel. If you take the panel out to have a look even better.