My MC is not very likeable at the beginning of my story, but I am writing her that way because her problems are real problems, not just the regular miscommunication types of problems that are common in my genre. I know that I might turn off some people, but the main point of my story is that she finds her way out of those real problems on her own, and gains some self-awareness in the process. And self-awareness tends to lead to likeability IMO.
In fact, my MC is the cause of some major pain and strife in her family due to her actions several years before the story starts. Not a death like yours was, but close to it. I don't think it makes her unable to be the MC.
I figure even if I am a miserable failure at this, I'll still sell one copy to my mother