What a jackass. I had similar issues briefly in the very beginning of my separation.
He would not respond to emails, he refused to email me or acknowledge any emails I sent him.
I asked him not to use bbm and if he would instead agree to text, he refused. I would text him, he would bbm me back. So very frustrating.
I don't remember exactly how I kept it together but not fighting about it or letting him know how much it bothered me was definitely key in my success. Eventually he found something else to be upset at/about and started being reasonable with me.