ok, guess I left the dome-light on too long... 

Starter cuts-out before it turns-over (long-story, let's just say some moron. [or greedo?] designed a system with a relay with too high a release-voltage).

Gotta get some more juice in that batt.

Have a jump-pack... Because of the relay, you're supposed to charge for a bit, rather'n jump... but either way, apparently that didn't have enough juice, either.

Third-option (skipped over the obvious one...): House-batt... Obviously, jumper-cables from house-batt to starter-batt.... Yeah, didn't think of that.

OTOH: house-batt is jury-rigged to charge (slowly) from main system through cigarette-lighter and a series resistor... And... it was plugged-in. So, house-batt-voltage probably equalled main-batt voltage. So, really probably doesn't matter that I somehow completely overlooked the obvious jumper-cabling in favor of:

Jump-pack has a 120V charge-input... to charge the jump-pack. House-batt has a 125W 120V inverter.

Yes, it *almost* sounds like a free energy scheme.

Yep. Then, the brilliant idea that rather'n wanting to charge the jump-pack, what I really want to do is charge the main batt... Now, I'm almost certain jump-packs aren't usually designed for this... but mine didn't complain, and the inverter never once turned on its cooling-fan... so, it's obviously not charging anywhere near 125W... right? (well, it is quite cold out, and in, that was the whole point of starting the engine... anyhow...)

So, about then, halfway in, I realize the jumper-cable possibility, then think of @Ted Yapo's attempts jump-starting a car from a coin-cell.

The key, here, is that the house-batt voltage could be [drained to] quite a bit lower than we need on the main battery to start. We Have A Boost Converter, maybe a bit like joule-thieving?

So, that combined with concern I'd blown a fuse in the jump-pack-charger, which might explain the inverter's silence, had me looking for ways to measure whether it was charging... yahknow, without having to move from my balled-up-trying-to-stay-warm position on my chair. 

First stupid attempt:  I built-in a jumper for that! Measuring charge-current to the house-batt. Zero. Shit, the fuse is blown. No, wait, the inverter draws 0.6A unloaded, and it's light is on... OH, Right... charge-current *to* the house-batt.

Now I'm debating unhooking yhe jump-pack from the main-batt to throw my meter between... but it's cold out there.

And then the obvious, again a bit late, but not too [late]: Reach all of 2ft and measure the friggin' voltage from the lighter-outlet, see if it's increasing.

Holy Snap... it hasn't even been an hour (Maybe half) and it's already reading 12.7V, 12.7, 12.8! Mind-you, we're charging two batteries, one of which is *significantly* larger than the charger was [likely] designed-for. And doing-so *in-system.* This is incredible!

So, on to testing The Ted Theory: House-batt is a steady 12.03V. YEAH! Joule-thievery! er something.

Disconnect... yep, 12.6, 12.5, 12.4... but pretty slow, surprisingly. And house-batt's like 12.1, now...

So, definitely charging. Friggin' awesome.

A few more minutes and give er a go... again lazy (mind you, it's 3:30AM at this point) and chilly, try to figure out how to remove the charger... I already put it through the wringer, starting with it connected would be cruel. But not cruel enough to step outside. What to do? Oh, huh... charger didn't have a switch... It's either plugged-in or not. And lo and behold there's a switch on the ol' inverter.

Crank it over... and here we are, now cozy-warm and lazy, still "topping off" three batteries--main, the jump-pack, and house-batt--from my alternator,

Man, this level of "lazy" might be borderline risky to these systems. I wouldn't recommend it. OTOH a well-designed multipurpose jump-pack with inbuilt-charger would be wisely-designed to handle AC charging of a car's main-batt. Nevermind fast pack-recharging from the cables. Guess I'm just used to low-quality stuff.

Sometimes things go alright!

(but, seriously, if my main batt had more than 12.03V on it, which it must've to have charged the house-batt to the level where it, *after recharging* the main-batt, still had 12.03V on it, there is ZERO justification for that relay's kicking-out. And, further, risking a $50 fee and mandatory servicing in so-doing! Nevermind being potentially dangerous!)