Sorry to be unsympathetic, but he's out shopping because at home all the cupboards are locked.
If you're both celibate by mutual consent, then he's very wrong but if you've made that decision on behalf of you both, then he's only doing what you predict in your original question.
You have to ask yourself why you cannot express and show any intimate love to him and fulfil his needs? If you want to save your marriage you'll need to get counselling or visit the doctor if it's a physical problem.
Re-starting a sex life is just the beginning, you need to explore each other and find out what blows his brains with a bedroom fireworks display!!! There's plenty of info on the net. And then keep working at it.
If you really can't bring yourself to be intimate, I'm afraid it's only a matter of time before he does get a successful hook up. Maybe you two should chat more about where you go from here. It may be that to save it you have to think about opening up your marriage and letting him have a 'buddy'.
If it's any comfort we've got the reverse problem. It's H that can't / won't, leaving me cross legged lol.
Maybe we should try out that TV show, wife-swap lol!!
Seriously. Good luck and do what you can to recover your mrriage.