The room was so full of smoke that I could barely breathe.
Literal
Room [topic-は] smoke [with-で] full [and-で], almost breathing could-not [to the extent of-くらい] was.
Chains でいっぱいで (full of smoke, and...) with the degree expression ~くらい (to the extent that). ほとんど~ない means 'barely, almost not.' The sentence builds from description to consequence effectively.