She wants to want to have sex - now what?

This is my first post here. Our dead bedroom has been a problem for years and I've been too conflict-averse to do anything about it, but it's no secret to my wife there's a problem.

Background. I'm 40HLM and she's 36LLF. We've been together for 18 years, married for almost 6 and have 2 children (4 and over 1).

We're had a dead bedroom for over 10yrs, neither of us really remembers how long, with the exception of when we were trying for a baby. Sex of some kind of another has averaged once every 2-3 months for most of that time, so 4-6 times a year. When we do have sex the quality is great for me, and I believe it is good for her too (I always make her orgasm through oral first, though in the distant past I may have been more selfish, I can't remember).

I've just talked to her about it for the first time since I'm at breaking point (struggling to sleep, concentrate, been rejected pretty regularly the last few weeks). I couldn't just stay suffering in silence any longer. I spent a few weeks writing a letter but in the end decided to man up and talk about it.

She says she doesn't have any sex drive at all, but she wishes she did. She says it sucks for her too because she wants to have a sex drive. She doesn't have anything she wants to try in the bedroom or secret kinks or anything.

I asked if maybe she doesn't find me attractive any more. She didn't really answer that but said she stopped touching or hugging me because in the past that always led to me wanting sex - this is probably the initial cause of the DB and dates back to some decade or so ago.

So I guess my own sexual neediness has caused her to be averse to intimacy of any kind with me (we honestly bearly touch each other even though I love her deeply and believe she loves me too). What can I do? Where next? We're left after that conversation with nothing to work on. I suggested we take sex off the table and cuddle some but she doesn't think that will do anything.