"How can I tell if the batteries have been compromised "
That's easy, they have been. You'll find that pretty much ALL the battery makers in the US will gladly answer the phone
and provide free tech support, even if you are just shopping
around. And their answers all tend to be the same, even if the details vary a little.
All of them will tell you that a wet cell takes permanent damage, permanent capacity loss, from sulphation after 90 days. The compounds that form precipitate out of solution and there is no way to get them back into solution, so the battery loses SOME capacity, some will say after 30 or 60 days, all will say by 90.
They also all will say that every time you deep cycle a battery, no matter what kind of battery it is, it takes some damage. Some claim their SLI batteries will be permanently ruined and worthless in as few as 6 deep cycles. Others say their deep cycle batteries can take 50-300 or more deep cycles. But again--they all agree that killing a battery, totally discharging it and then letting it sit discharged, will permanently reduce the capacity.
So the only real question is whether your batteries are so badly damaged as to be junk, or have some useful life left in them.
And the only real way to find that out, is to put a charge on them, cycle them a couple of times, and load test them to see what capacity is left in them. I wouldn't bother putzing around with a store, where they may fast-charge them and damage them further, or prefer to scrap them to sell you new ones. I'd buy a charger of some kind, even a 6-amp car charger for $25, put a slow charge on them one at a time, let them sit overnight, check 'em out, repeat twice. You'll know whether they are or aren't any good, and you'll only have spent $25 for a charger you can always use on the car anyhow. Just make sure the charger CAN be used with a dead battery, because many of the new electronic ones are designed so that they will not even begin to charge a battery under about 10V, as a safety
Got a neighbor that can lend you a charger?
The distilled water
, btw, is about $1.50/gallon at the supermarket. No big deal, and if you can't find distilled used "deionized" in the laundry