By turning on the heater blower, you added a slight increase in electrical power required, and some connection, fuse, or relay could not handle the load. Since your battery did crank the engine before you turned on the heater blower, I would assume your battery is ok.
As BILL1734 suggested above, I would start by cleaning and tightening all battery connections. While cleaning battery connections, look for internal corrosion within the ends of the battery cables also. If no joy, then I would clean and tighten all grounds, followed by checking fuses, etc.
Good luck, and let us know the solution.
Fred
