The 61-year-old BBC commentator injured his arm and suffered bruising as he tried to stop the thief fleeing in his S-Type Jaguar by clinging on to the bonnet.
But Young said that although he had identified who he thought the robber was, it was not enough for prosecutors to proceed with the case.
It is understood the charges were not pursued after a witness was unable to provide evidence that would allow the case to go ahead.
Next Saturday's game might be the 138-year-old club's last after owner Vladimir Romanov admitted the Tynecastle club faces a winding-up order about £450,000 due to Her Majesty's Revenue and Customs (HMRC).
The latest crisis to engulf Scottish football came nine months after the Edinburgh team's former Scottish Premier League (SPL) rivals Rangers went into administration over an unpaid tax and PAYE bill.