My immediate suspicion is that 50 amps isn't enough to start a car. If you let the 50amp charger charge the car for a while and the battery still has some life left, it may for example put 500 amp-seconds over 10 seconds at a current of 50 amps into the battery, which the battery will provide back as 500 amp-seconds @ 1 seconds and 500 amps. 500 amps for 1 second is plenty to start a car.
Now, if the battery is dying, there will be a point where it doesn't accept even the 500 amp-seconds needed to start the car.
In the best case, the battery is just nearly completely dead, so that it provides enough juice to show the dashboard lights but not enough to even start rotating the starter motor.
In the worst case, your attempt to start the car with feeble buffering in the electrical system (dying battery), some electronics in the car may have been damaged.
What you did was wrong. Don't attempt to start a car with a charger attached on it! If the battery is suspected to be dying, continuing to drive with the car may damage the electrical systems of the car as the dying battery provides less and less electrical buffering, and some day an electrical spike from the alternator zaps something expensive!
To me, it was clear the battery was dying and it should have been replaced.
Replace the battery and hope for the best...
Edit: only afterwards did I notice that the battery was replaced with a new one two months ago. It may be the case the alternator is not charging it properly, causing even the new battery to die. Two months of too little charging can do pretty serious damage to lead-acid batteries that don't want to stay flat for an extended amount of time.
So, my advice would be to (1) charge the battery slowly, trying to salvage it, (2) load-test it with an automotive 12V bulb to see how many amp-hours it has (beware, the bulb will become hot!), (3) if you can't salvage the battery, replace it, (4) find the root cause of your battery failures, may be related to the alternator.
A long time ago, I had a 1989 Opel Vectra that was reluctant to start. Suspected the battery, but wasn't the battery. The cause was a broken ECU relay.