My 3 year old A80 has recently begun to drain batteries at an absurd rate.

I have actually had this happen before but you aren't going to like my solution; I put the cmaera in a drawer for about 6 months then one day took it out charged some batteries and put them in just to see if it would work and it did, and has worked perfectly fine sinse. I am sure that is some fluke tho. There must be something mechnical draining the power or thinking the power is drainly, mostly likely. I would say the only thing to do after trying to clean off the metal tabs where the batteries connect is to get it serviced. Sadly 3 years has become old age in the digital camera world.