I ran as fast as I could, but I didn't make the last train.
Literal
As-much-as-possible fast ran [but-が], last train [to-には] was-not-in-time.
Subject is dropped entirely. できるだけ ('as much as possible') modifies the adverb 速く ('fast'). The sentence-medial が is the adversative conjunction 'but,' not the subject particle. 間に合う takes に for what you're trying to make it in time for.