Though they found no cause of death (mēdemian aitian thanatou heurontes). Second aorist active with usual negative of the participle. As a matter of fact the Sanhedrin did charge Jesus with blasphemy, but could not prove it (Mat 26:65; Mat 27:24; Luk 23:22). At this time no Gospel had probably been written, but Paul knew that Jesus was innocent. He uses this same idiom about his own innocence (Act 28:18).
That he should be slain (anairethēnai auton). First aorist passive infinitive, the accusative case, the direct object of ēitēsanto (first aorist middle indicative, asked as a favour to themselves).