In any case; used to return to or emphasize the main point—'anyhow', 'anyway'.
何しろ時間がないから、手短に話します。
Anyhow, we don't have time, so I'll speak briefly.
彼は経験が浅いが、何しろ熱心だから期待できる。
He has little experience, but in any case he's enthusiastic, so we can expect good things.
何しろ初めてのことなので、まず様子を見ましょう。
Anyway, since this is the first time, let's watch how it goes.
Because; since; used to give a reason or explanation—similar to 'after all' or 'because'.
何しろ彼女は医者だから、病気の相談に乗ってくれるよ。
Because she's a doctor, she'll give you advice about your illness.
何しろ天気が悪いので、遠出は中止になった。
Since the weather is bad, the trip was cancelled.