The room was so dark that we had to grope our way to the door.
Literal
Room [subject-が] too dark was [because-ので], we [topic-は] groping [with-で] door's place [until-まで] proceed must.
A longer, more complex sentence. あまりに~ので means 'so much that' — expressing an extreme degree causing a consequence. 手探りで (groping, feeling one's way) is a vivid te-form used as an adverb. The whole sentence builds from cause to consequence with natural flow.