Codes to repair question

[Nightmaro]

My car just took a dump, a 1999 Camaro V6. I was driving it, parked for like five minutes, then it would start and immediately die- if it actually started. Yes, my check engine light was on, but I have come to the conclusion that this is a Camaro condition, as my 85 and 94 had the errant light every now and then. We replaced the ignition coils, as two of them had already gone bad and seemed to be similar. Now, it won't run at all and we ran the codes and got P1514, P1516 and P1404. Even though AutoZone does diagnostics, they told me to take it to a garage because they couldn't guarntee me that a new mass air flow sensor was the problem. Can anyone please give me some input on this? My car has been sitting for over a week and I'm in withdrawal. Thanks!