verb → "want to" → "don't want to" / "didn't want to" / "come to want to"
行く → 行きたい → 行きたくない / 行きたくなかった / いきたくなる
食べる → 食べたい → 食べたくない / 食べたくなかった / 食べたくなる
行きたくなった is the past form of that last conjugation, 行きたく becomes like an adjective describing the state of wanting to go, and なる is the verb modifying the adjective (in this case, in the past tense).