I've run clean out of money.

Literal

All-money entire become-nothing-[completive-しまった].

有り金 ('money on hand, ready cash') — literally 'money one has' — is a somewhat old-fashioned compound. ~てしまう / ~てしまった marks the completive aspect with a nuance of regret or finality — 'have gone and done X,' 'unfortunately X happened.' Here the speaker is rueful about having no money left. 全部 ('all, entire') intensifies the loss.