Thanks for all the part numbers etc, thats really useful.
It certainly seems like you're using the right battery. Or at least the Battery 02K6692 is listed as the correct one. can't find a reference for the 02K6693, but I don't suppose it's much different, if at all, to the other one.
I gather from your original post, that at least one of these batteries is (or was) brand new, right? I assume you did follow the correct charging procedures when you first had it? i.e Charge initially for 12 hours (or thereabouts), use till fully discharged, then repeat this another 2 -3 times.
Also, when you performed the very first 3-4 charges on the brand new batteries, were you using the replacement power supply at that time or the old one?