Starter Solenoid problems of the 1999 Toyota Corolla

Currently I own 1999 Toyota Corolla , model -ce which was originally used vehicle and was @8500 miles on it at the time of purchase. Car was in good running condition until on 8/29/09 car stopped suddenly while moving and smokes came out from engine hood. Without wasting time, insurance company was contacted immediately and car was towed to the repair shop. Repair shop personnel inspected quickly and I was told that wiring of the harness cable near the engine has been overheated and some have melted due to malfunctioning of solenoid on the starter which also caused battery to be overheated. I touched hood and it was very hot. We were lucky on that day otherwise battery could have exploded should we would have tried another attempt to start a vehicle. I had my wife and two kids in the car. As of now, repair shop is not sure about total extent of the damage and asking @$736. 00 includes replacement of battery and starter as well as labor towards finding, replacing by soldering misc harness cables. After doing this much, they will check again the vehicle to make sure problem is resolved, otherwise they have to continue to chase until car is fixed. This leads to uncertainty of cost and reliability of the vehicle even after repair. This event could have resulted into tragic incident for my family where my wife and two kids were in the car during the event. As of now, I was advised by original car seller rep, repair shop and few friends to sell it off in as is condition or after repair. As of now, car seller is offering $300. 00 for the car in as is condition. I am still wondering while wires overheated suddenly and smoked. I just did oil change a few days ago. Per insurance company, this damage is not covered under insurance and have to take care personally. This is a huge cost burden with unknown reason.