It is worth noting that the original Flash version is widely considered the "beta" or "prototype" for the modern game, The Binding of Isaac: Rebirth.
You’ve downloaded the repack. You’ve unblocked it. Now you’re in Basement I with one heart and a tear rate of 10. Good luck.
Sites like "CrazyGames" or "NewGrounds" (where Isaac was born) have archived versions. Search for "The Binding of Isaac NewGrounds archive." These are technically "unblocked" because they are web-based. However, they usually run the pre-Wrath 1.0 version—no Sheol, no Greed mode. The "Wrath of the Lamb" expansion was never officially released as a free web game.