Electrical problems PLEASE HELP
 

So I have a serious electrical problem. I have a 2010 Lancer GTS with the F.A.S.T Key system. It started by my car intermittently not starting. The first time it happened, I brought it to a local shop and they said it was the starter. I got a new starter and that wasn't the problem. Then I thought it might be my fob because coincidentally, it died at the same time but my thoughts behind it were that I could just use the key to start it but that wasn't working so I changed the battery in the fob and it started. So I went home and the next day, went to work and after work stopped in at a store and it wouldn't start again. After a bit of time, I managed to get it started and afterwards, I was able to make the problem happen over and over again by trying to start it and stop it over and over. maybe 1 out of 10-15 times would it start. The next morning I brought it to the dealership. They said they went through the ecu and tried to reprogram it but it wouldn't stick and they apparently looked into everything. The're at the point where they believe it's a problem with a broken wire between the ETACS and the ECU. This is coming from the Engineers at the Corporate office in Toronto. I find this really hard to believe and I feel like this dealership can't figure it out and they just keep wasting time on the wrong things. They are billing me by the hour to diagnose the problem because they have no idea what it is. So far they have 16hrs on the car and thankfully I only approved 4 hours so I won't get billed for the entire 16hrs but to proceed they say it might take a couple days and that's only to find the problem. Does anybody have any experience with this or what do you guys think?