I'm afraid I haven't got any answers but just wanted you to know some of my experience in case it helps.
Also, wanted to share my experience for those of you who think men are 'always' up for it and coping without sex is not as bad as being 'obliged' to have it.
Cutting v long story short. I have a great marriage, I truly love my husband, he is my soulmate, my best friend, he makes me feel loved and cared for, we have a laugh, his is affectionate, cuddly, hand holding, kissing, we share our thoughts and feelings, we have 2 wonderful children and he slogs his guts out to look after me and the kids.
However, he has a very low sex drive and I have a very high sex drive. I knew this getting married but thought I could cope with it. I can't.
His lack of initiation, interest, passion and constant (kindly) rejection has left me with major body and confidence issues. I feel unfeminine and frustrated to the point of screaming.
We have tried everything to try and sort it out, discussions, rows, talking about it, not talking about it, weekends away, sexy underwear, rotas, sex agreements, no sex agreements, crying, screaming, letters, other friends speaking to him about it, me asking if I can get it elsewhere, just agreeing that we would be platonic and there is no answer. As someone else said, he doesn't want sex so that's it!
Like the OP I don't think he is gay (i have asked him several times). In his words,he just isn't 'bothered' about sex. He likes it when he does it but other than that doesn't really think about it. He says it never occurs to him to initiate it cos he never feels horny. He also says that is he constantly stressed about money and exhausted by the kids (i think some of this is an excuse though). At the end of the day, like many women out there he just has a low sex drive.
I don't have any answers for the OP but just wanted to add that maybe it's nothing as deep as being about your rape etc...i'm guessing he just has a low sex drive and like my husband, is genuinely exhausted by kids.
You will find 100 women on here who can relate to those feelings. Women who feel stressed and tired all the time and as happy as they are with their husbands they really couldn't care less whether they had sex or not again.
big hugs, it's a horrible situation to feel sexually unwanted.