Following on Tom's excellent guidance...
My car suffered a gradual deterioration in starting. I travelled a lot for work, and while I was gone I left a maintainer plugged in. But if i drove it a bunch sometimes it would struggle cranking. Meter readings showed everything was OK as far as charging and voltage drop. I ended up with long test leads and a few meters, looking for voltage drop in some of the primary cable sections. I replaced the positive cables, which run from the battery in the back to the starter, then forward to the alternator, the ABS unit, and on via an engine bay jump post to the central electrics panel. All new. but still seemed to have trouble charging the battery. Scratched head where hair used to grow, but that didn't help. More research turned up a recommendation about the ground strap between the chassis and the battery. Mine 'looked' fine, and when testing with a meter while cranking it measured fine. I replaced it anyway, and the charging issues disappeared. Corrosion in the copper strap braid inside the protective shrink sleeve wasn't obvious until I cut it apart.
Replacement is a tinned-copper braided strap, with shrink sleeve to protect it as it passes out of the box, past the spare wheel and cover, and finally to the rear apron and crossmember. It's the same spec that ABYC demands for on-board marine duty, but has a regular battery post clamp on one end. Marine installs always have lugs rather than clamps. Anyway, a 2ga-equivalent strap solved the problem.
For your half-charged battery, connect a smart charger/maintainer directly to the battery posts, and see if it 'comes back'. Mine gets an annual test for specific gravity, usually a good indicator of slowly deteriorating batteries. A little floating-balls tester is under $5 at the local Wal-Mart. I use a more interesting industrial-strength unit from a NAPA store, one with a graduated float that gives actual density. The floating-balls one is easier, faster, tells me what I need to know, and is much easier to clean after I use it.
Poor wiring, corrosion and connections force the alternator to work harder to charge the battery. Batteries really don't like to be anything short (sorry...) of full charge, so living with poor connections and corroded wires will cost you in both alternator and battery life.
I ended up buying a couple dozen of those plated straps, and offered them to area owners when I held regular clinics at our home above Los Angeles. Great stocking stuffers or door prizes, in case you are looking for a thoughtful gift as the holiday season looms larger again.
For the person who has everything though, I still recommend a large dose of penicillin to start...
