Electronic – Stabilize 12V to 12V

Your dumb charger is just providing a slightly regulated voltage. It works due to the combined resistances of the charger and battery limiting the current. As the battery voltage gets close to the charger, the voltage potential is less. So with a fixed resistance, the current drops.

I doubt that you can modify your current charger to push 38 A up to 14.4 V. This could only happen if the combined resistances and voltage difference allow sufficient current flow.

Most likely you will need a higher voltage source and then circuitry to make a constant current source to provide a fixed amperage. Shutting it off can be done with a simple comparator circuit. Put a 10k trimmer pot across the battery voltage and run it into a comparator along with voltage from a zener regulator. Then you just adjust the voltage divider from the pot till it trips at the correct battery voltage. Use that to turn off a high current MOSFET or something similar. (Might use the same MOSFET to control the constant current.)

Ouch. My best guess is that your battery is toast.

Lead-Acid batteries suffer from several damaging chemical processes if they are allowed to remain discharged for long periods of time. One of the real problems is something called "Sulfation". You can use Google to search out that term and also look at the many attempts to build de-sulfation devices. Wikipedia has a good description of the problem: Wikipedia

In general, I have good results with Lead-Acid batteries so long as they are kept charged. We build our own chargers: Equalize voltage is 15.0Vdc and float voltage is 13.5Vdc. The battery is charged with constant current until the current drops below the current limit value, then the charger drops into float mode. There are better 3-stage chargers available now but we have had great success with those chargers - some of that gear is more than 20 years old and the users routinely get 5 to 7 years of battery life.