Car Stall problems of the 2006 Lexus IS

My vehicle stalled at a red light and would not restart. After being towed to the dealer, they came back with a diagnosis of massive carbon build up. They advised that I reach out to Lexus corporate to determine if there was any support I could receive. After several weeks of going back and forth, Lexus corporate refused to provide any assistance because the car could not produce any of the necessary trouble codes to qualify for their customer support program surrounding this Issue. After much hesitation, I agreed to pay $700 to have the top cleaning done. After top cleaning was complete, the dealer calls to report that the car still wouldn't start and they didn't know what was causing the Issue. Now they have an "expert mechanic" from Lexus corporate coming out to inspect the vehicle and determine the problem. This took another 1 1/2 to 2 weeks to complete. I received a phone call from Lexus corp, that the Issue was now a timing chain that was going to be $1200 to replace. When I spoke with the dealer, they agreed to credit back my $700 from the misdiagnosis but quoted that the timing chain would be $1700, not $1200. After several days of haggling, I finally agreed to pay $1350, only to get another call from the dealer now saying that metal shavings have fallen down into the engine block and the entire engine would need to be replaced. Although I have all of my service records, Lexus Is trying to pin the blame on me, stating "lack of oil changes". My vehicle's year, model and date of service are all qualified to be covered under this warranty. This car has proven to experience these problems associated with this recall and because the engine Is in such bad shape and Is unable to produce any codes, they are refusing to honor this warranty. This has now been going on for nearly 3 months and I still have no car and no resolution in site.