Try this. : With the engine off read the battery voltage at the battery with a DC volt meter. Should be 12 volts DC, probly less. Start engine. Should read ~14 volts DC. If it is still ~12 your alt is FUBAR. If when not running it is like 8 volts your battery is suspect.
If you have a ground that is draining your battery witht eh engine off then you need to set up an ampmeter to read the battery discharge witht the engine off. You may be able to find a clamp on DC amp meter if you have an electrical type as a friend, Otherwise you will need to go to the auto parts store and see if they have a shunt and meter to install for testing. Then you can disconnect things one at a time and look for the ground.
Or you can try disconnecting a battery lead next time you park and see if it will start later by re-connecting it.
Pull my finger