Do you have a battery charger? If so, what happens if you start-boost the battery? If you can get the battery running, measure voltage at the battery with a multimeter to see what the charging voltage is. It should be over 13 volts. If not, the alternator could be bad. Also when the engine is off, try to rotate each battery cable, near its post connection but do not touch the metal clamp or post. If you can, the clamp is not tight enough.
If measuring battery voltage with the engine off shows less than 12 volts, the battery could be bad and should be load-tested.