i am very sure that the batterys are dead. APC recommends to change the
batterys every 3 to 5 years. I'd change them every 3 years to be sure.
Its very unlikely that your 6 year old packs are still fully functional.
I had the same symptoms at a customers APC (3000VA) and the battery
packs were dead. Try to locate the packs on ebay, can save quite a bunch
of money (but beware of low quality packs).
I've used them multiple times and been very happy.
I have used them as well and been fairly happy. Beware that they will spam you to death (and responding to their mailings with removal requests continue to go unanswered).