Why did you have to charge the battery?
If the alternator is doing its job, the battery will be charged, unless it sat for prolonged amount of time. If not, the engine running will drain it fairly quick.
Do you have access to a multi meter? If the battery has about 12.5v charge to it, and the cables are good, and you hear a clicking noise from the starter when turning the key, it could be the solenoid on the starter that's bad. Does all the interior lights, radio, etc work alright?
If the battery and starter are good, then the power isn't getting to the solenoid. That could be a loose cable connection or a bad cable.
If the alternator is good, it will read about 14.7v at the battery when engine is running. But since you can't tell that right now, it needs bench tested to confirm.
First check all your cables for loose connections, corrosion, breaks. If good.... time to remove the starter and bench test it, then the battery, then the alternator. Most parts stores will do this for free. If all test fine, then a bad cable is suspect from inner corrosion.
