Getting the battery tested is a good idea. Did you happen to try starting the car immediately after charging the battery, or only after it sat a couple of hours? If the battery charger says the battery is charged but it won't provide enough current to start the engine, the battery may have a high internal resistance. Bonus points if you connect a multimeter and monitor what the voltage drops down to when trying to engage the starter motor. With the meter still connected to the battery terminals, if the engine starts and runs you can also get an idea if the alternator is working properly by measuring both the DC voltage and AC voltage at the battery. The DC voltage should be between 13.8 and 14.4 V after just starting the engine and the the AC voltage should be near 0 VAC. I'm not sure off the top of my head how much AC voltage would be considered too much and indicate a bad diode.
You could also disconnect the battery, charge it, let it sit a couple of hours, then reconnect and see if it will start the car to determine if there's an internal low resistance path causing the battery to self discharge.
High internal resistance or an internal low resistance "short" would both be battery defects and should be fully warrantied by the place you bought the battery from.
-Rod