Battery draining very fast
Sorry to be the bearer of bad news.

As you suspect, the one battery that was connected backwards has been damaged and needs to be replaced.

For the other batteries, the situation isn't as obvious. If the charge voltage was applied over three batteries instead of four, it could have overcharged them all. If your batteries were standard lead-acid or SLA (sealed lead-acid), then you should open the caps and check to make sure the fluid levels are correct.  Since you are using AGM, however, they are supposed to stay sealed.

Assuming that these three are fine, there still may be a problem trying to match a new, fourth battery.  If the new one has slightly less capacity, it will become depleted first, and may become damaged if the system gets severely discharged.  If it has slightly more, it can cause a similar problem with the other three, although it will be more forgiving.

Here's what I would do:


Get a new battery from the same manufacturer.
If they were SLA's or standard "flooded" lead-acid types, check the fluid levels on the three "good" batteries. (don't do this for your AGM's!)
Using some other charger, charge each battery individually .
Allow them to sit for 12 hours or so to stabilize.
Measure their voltages, and make sure they're all close.  Remember, the charger had brought them all to the same level.
If all looks good, go for it!


After allowing the system to discharge a bit, check the individual voltages again an make sure nothing is getting severely unbalanced.  Worst case, you may have to buy four matching batteries.

Good luck :) 

P.S.  I had originally stated that you could top off the levels in an AGM battery, just like a standard flooded battery.  I was incorrect: AGMs shouldn't have loose liquid sloshing around.  At an earlier company, we had, in fact, done this to a compromised AGM.  It worked, so we though it was the correct thing to do.  It turns out that we basically converted it into a poorly-designed SLA :)