"Doesn't start" can mean a lot of different things, but since a push-start worked, I'm going to assume the starter wouldn't crank the engine. Correct me if I'm wrong. That, along with the other symptoms points to a failed charging system and the battery has run down while driving. You should have seen a warning light on the dash or the "Volts" gauge would have been dropping. The headlights would have been getting dim too.
If all of this sounds right, start by measuring the battery voltage with the engine off and with it running. Off, it must be 12.6 volts. If it's around 12.2 volts, it's okay but discharged. If it's near 11 volts, it has a shorted cell and must be replaced. With the engine running you must find between 13.75 and 14.75 volts. If it stays the same as it was with the engine off, the generator, voltage regulator, and associated wiring are suspect.
Also, follow the smaller battery positive wire to the under-hood fuse box and be sure that connection is clean and tight. Those commonly work loose on all car brands.
Sunday, January 5th, 2014 AT 12:59 AM