[verb (dictionary form)] + だに + [predicate] [noun] + だにしない
だに means "even": it marks the least you could do and says that even that much has an effect, or doesn't happen at all. It is literary, and it lives in a handful of fixed phrases. After the dictionary form of a thinking verb, it means "even just to …".
The verbs that take it are few: そうぞう想像する, かんがえる考える, おもう思う, おもいだす思い出す, きく聞く. The point is that the real thing would be worse still.
After a noun, usually a する-noun, だにしない says not even the slightest of that happened. The set phrases are びどう微動だにしない "not move a muscle", よそう予想だにしない and そうぞう想像だにしない "never even imagine", and いっこ一顧だにしない "not give a second glance".
The verb is a noun or a dictionary form, never a ます-stem.
だに belongs to novels, essays and news writing. In speech, さえ or だけで carries the same idea: そうぞう想像するだけでこわい怖い。 For だにしない, everyday Japanese says ぜんぜん全然うごかなかった動かなかった or ゆめにもおもわなかった夢にも思わなかった.