How did you test your battery? If you stuck a multimeter across it then it won't you ****. A battery needs a load applying to draw a current and cause a bolt drop. The best way is with a battery tester, or if you don't have one, two people and a multimeter. Stick the meter on the battery, DC volts, then get your oppo to turn the engine over. That will give you the battery voltage.
As for testing the alternator, do all the above then when it starts check the voltage, if its charging it will be between 12.7-14v.