Was this self installed iinstalled or installenstalled by a contractor?

This sounds like a defective battery, charger or wiring. It would appear to be a potential warranty issue. If it was installed by a contractor, notify them.

I recommend reading the Zoeller instructions. I suspect the Troubleshooting section has your situation. Link here.

If everything looks normal, you might want to test the battery voltage with a multimeter. If the battery is very low or not holding voltage, it could be the issue. Otherwise, the charger itself may have a problem. At that point, contacting Zoeller support or checking the warranty would probably be the safest next step.

It sounds like your battery went into a "deep discharge" after sitting unplugged for so long. The heat and smell mean your charger is struggling to revive a battery that likely has a lot of internal resistance.

Here is a practical way to handle it:

Isolate the Battery: Unplug the system and move the battery to a well-ventilated area (like a garage). If it’s off-gassing, you don't want those fumes in your basement.

External Charging: Don't use the Zoeller unit to jumpstart this. Use a standard 10-amp automotive charger to see if the battery will even accept a charge. Smart chargers like the Aquanot often "error out" or overheat when trying to charge a completely flat battery.

Get a Load Test: Once (and if) it reaches a full charge, take it to an auto parts store for a free load test. If a battery sits at 0% for months, the plates usually sulfate. Even if it says "12V" on a meter, it might not have the "juice" to actually run the pump for more than a few minutes.

Check the Charger: Once it has cooled down, check the plastic casing for any warping. If it smells like burnt electronics rather than just hot dust or sulfur, the charger's internal transformer might be fried.

I’d leave the charger unplugged for now, especially since it got hot and there was an unusual smell. I’d have the charger and battery checked before putting it back into service, since you want to be sure both are functioning properly before relying on the backup system.