2009 (7th Generation) Chev Malibu Hybrid ONLY RUNS WHEN STARTER BATTERY IS CHARGED AND STOPS RUNNING WHEN STARTER BATTERY IS DISCHARGED.

We bought a 2009 (7th Generation) Chev Malibu Hybrid; we got it really cheap and expected to have to affect repairs in order to get it road worthy.

Unfortunately the seller is a .gov entity so obtaining any info about the vehicle is virtually impossible.
I'm new to the hybrid vehicle scenario and am learning quickly.
The situation I have with this particular Malibu seems rather odd to me and may be of interest to the seasoned veteran hybrid owners out there and at the same time I may gain some insight on how I should proceed with regards to getting this vehicle up and running nominally, if possible. So without any further introductions I would prefer to get to the interesting parts of my post:

When we picked this car up it was stone cold ded. So, being the amateur that I am I figured the battery is ded. Well, of course it was, so I did what any normal 'newb' would do, I got the jumper cables out and jump started it. It started right up and when I took the first jumper cable clamp off of the battery it immediately stalled. After 3 tries with the exact same results I ran off to the local walmart and got a replacement 12 volt starter battery and after installing it we were "off to the races", so to speak. Everything was going fine, terrific actually but we were in a huge city (think Phila) and it got dark so we were doing a lot of stop and start traffic with headlights. So we got maybe 20 or 30 miles and it left our driver sitting, he fortunately had presence of mind to turn off into a neighborhood when it started to 'malfunction', i.e. lost power steering, lights, engine power, etc. We had a 3 vehicle convoy going and we kept the Malibu in the center, just to clarify for anyone who may be curious. So at this point I'm not sure exactly what reasoning I was using, it was high stress enviro, had get-there'itis (home) with two uninspected but registered and insured, 'half lit motor vehicles, in "think-Phila" with a 3 hour higway trip ahead. So I was burning years away with stress levels that were off the meter. I believe the thought was that the alternator wasn't charging buit I didn't bring any tools for that type of diags. So I did what any 'stressed out newb who will never give up would do', I went to the nearest 'huge box store' and bought 2 starter batteries, with an eye on getting everything home and then returning the batteries or exchanging them for something that we might need, like food and groceries for our children in the family. So, luckily my son, aka 'the driver', once again, had presence of mind to mark our breakdown location on his GPS or we would have never re-located the vehicle and I came back with two new batteries and connected the freshly dead battery to the '2-battery' system that I have going on in our Dodge Caravan to recharge. (The extra batteries I brought with me were deep cell batteries that wouldn't fit into the battery compartment (more on that later)). So, put new batt #2 in and off we went, headlights on and out of the BIG city. We made it all but exactly 100 miles on city rated interstate (turnpike) before we had to swap out battery #2 for battery #3, which got us about 140 miles on medium traffic interstates before batt 3 gave up the ghost. At this point we were only about 30 miles from home and were broken-down on a low traffic, high speed superhighway; squeezed right up against the right guard rail and about an inch between the driver side door and the right fog line. Traffic was whizzing past, tragically close, with each passby, just inches away and followed by a huge blast of wind; so I did what any 'desperate newb with get there 'itis" would do: I put my biggest 12 volt deep cell battery on the front passenger side floor, cracked the front passenger side window, ran the jumper cables through the front passenger window, into the engine compartment and connected the other end of the jumper cables to battery #3's freshly depleted, terminals. Then I announced to my bewildered and highly entertained driver, who was actually on leave from the armed forces, to 'lets get going' and no Sleep til Hammersmith (meaning don't stop unless you have to). That last battery swap, actually a 'running jump', got us home, with myself exhausted, and perhaps just a slight case of added PTSD from the stress associated with having to make an H Ross Perot-like vehicle (you never know if its going to run) make it home.

I realize that this was a long story but I wanted to tell the story in order to help convey what issues I'm having with this Malibu. I don't have to tell everyone that the journey was a five thousand yard stare, dilated pupil, 'white knuckle' drive (and I was driving the 'known good vehicle' while my driver seemed to be having a 'time of his life' and I swear he enjoyed every second of it, somehow... (sort of like a skydiving and bungee jumping thing...)

In summary this 2009 Chev Malibu, ex-gov (probably police), motor-pooled automobile has the following symptoms:

1) It runs if the 12 volt starter battery (in the engine compartment) is charged up and when the starter battery goes ded, the lights, power steering and all of the accessories stop working followed by the engine, which consequently will leave you sitting where ever it happens.

2) I used an OBDII code reader to ring out the stored codes from the vehicle's onboard CPU and they are as follows:
A) P1A26-Powertrain
B) P1A59-Powertrain
C) B2AAA-Body
D) P0A92-Powetrain
E) P0AFA-Powetrain

3) I am planning on repalacing the 'propulsion assist' battery (behind the back seat).

Does anyone have any advice on how I should proceed?