Sorry about the late reply.
A couple things I noticed:
Once you shut the engines down, powered up the APU and APU GEN and motored the left engine, you moved the left engine to idol and the the right engine to idol shortly after. You can only start one at a time (unless you are doing a windmill restart). The biggest thing I noticed is that you were in a rush, I know it's a little concerning that you have two engines not producing thrust, but you need to slow down and follow the steps. I believe you actually had the left engine started toward the end and ended up killing it by moving the throttle forward too soon. I let your track run again right up until the engines failed, then I took over and restarted both engines. I'll post the track in a bit so you can watch how I did it. Just keep in mind that I have a second monitor and a TM WH, so it doesn't really even look like I look at the gauges or switches much, so you probably should hit F2 and then back to F1 so you can pan around the cockpit and see what I'm doing.
If you need, we could get on ts\vent\steam and I could walk you through it in game, just PM me.
Track added. One thing to note, tracks don't always play back correctly when I record them on my machine. So If I appear to say, not even try to start engines and fly into the side of a mountain... that's probably why. I did watch it and it replayed fine on my machine though. Hope it helps. inversion recover.trk