I've done that many times with "modern" chargers. First, check the battery voltage when it won't start. Cheapo digital multimeter from Harbor Freight is usually less than $10 and accurate enough for this test. Check a known good, fully charged battery. It should read about 12.6 volts if full. 12.3 is partially charged and it drops from there. An ammeter (mine has a low amps setting. Read the directions) between the removed battery cable and post will show if there is a draw.
Interior light NOT going off will drain the battery. Mercury switch for the under the hood light will too. Missing a ground wire from the battery negative to the body (one to the motor can't feed back the lights, etc without it) will cause undercharging too. While running the alt should be making about 13.8-14.6 volts at idle depending what accessories are turned on. Loose or worn too narrow belts can cause slippage (even without noise) and not allow the alt to charge.