If you are not connected to any unflipped Coal Mine, you can still purchase coal from the Coal Market, provided you are connected to a Merchant space with a coal icon (Warrington, Shrewsbury, Nottingham, Gloucester, or Oxford).

This is supported by the following rules:

• From page 9:
  "If coal is required, the location you are building in must be connected to a source of coal (see 'Consuming Coal' and 'Connected Locations')."
• From page 8 under "Consuming Coal":
  "If you are not connected to an unflipped Coal Mine, you can purchase coal from the Coal Market, starting at the cheapest price. This requires a connection to a [coal] icon (shown on the Warrington, Shrewsbury, Nottingham, Gloucester, and Oxford Merchants around the edge of the board). If the Coal Market is empty, you can still purchase coal for 8 / ."

Summary

• If you are not connected to any unflipped Coal Mine, the build action is still valid as long as you are connected to a Merchant space with a coal icon, allowing you to purchase coal from the Coal Market.
• If you are not connected to any coal source (neither a Coal Mine nor a qualifying Merchant space), you cannot build the Industry tile that requires coal.

Source: page 8 and page 9

Source: Core Rulebook (pp. 10, 8, 9)