I've got a 1986 Volvo 740 GL, 4 -cylinder, non-diesel non-turbo. I'm having a hard time figuring out why I can't get the thing to start all of a sudden. I'll detail what happened, and what I've done so far to troubleshoot it.

WHAT HAPPENED
I was driving home and the car just turned off. No chug-chug-chug or slow sputtering before dying (so I'm guessing not a fuel delivery issue), it just turned off, I coasted into an apartment complex driveway and stopped. Tried to start it, lights come on on the dash, it's turning and turning but won't turn over. After three or 4 tries the lights on the dash look a bit dimmer.

I try a jumpstart, it doesn't work on the first try but starts on the 2nd try. I disconnect the jumper cables, let it idle for a minute, then it turns off, same deal, turns and turns but won't turn over. Try jumping it twice more, it fires up, holds the charge long enough for me to drive home. Next morning .... same thing, won't start.

WHAT I'VE DONE SO FAR
I pulled the battery, took it to Battery Exchange, they said it was weak and they charged it for 24 hours, said it's fine. I pop it back in my car, it fires up fine. I take a 2- mile drive, park for an hour, starts fine, go to the market 3 miles away, park, starts fine but after idling for a minute it turns off. Start it again, it fires up, I get home. Next morning, won't start.

Pulled the alternator, took it to AutoZone, it checked out fine. The voltage regulator is internal in the alternator, but they didn't have the cables to check if it was good. The positive battery cable had cracked insulation near the battery, so I put on a new cable ... the old one was cracked a bit near where it attched to the starter (enough so the copper inside looked faded, not shiny like new copper).

Try to start it, same thing, sounds like it wants to turn but just won't turn over. Spark plug cables, distributor cap and rotor are less than a year old, don't see any cracks anywhere. Checked for spark at the plugs and at the ignition coil, got spark. Tried a jump-start, no dice. About a half hour after trying the last jump, being that it was 2am I tried starting it for giggles, and it barely tried to turn like the battery was MORE drained than before.

I'm thinking the voltage regulator isn't an issue since I don't think it would prevent a jumpstart from working. I was thinking that the guys that charged my battery didn't realize it truly was no good anymore (about 3 years old though) since they didn't put a load on it by slapping it in a vehicle to see if it would run something, but they hooked it up to a meter and said it was fine after the charge ... but if it were an issue with the battery I THINK the car would have started with a jumpstart, esentially starting using the other car's battery.

I'm no expert on auto repair or electrical diagnosis, but I've tried what I can think of. Is there anything else I should try before having the car towed somewhere to troubleshoot a short?

Any help or advice is greatly appreciated. Thank you!