Air Loop Heating Load is zero

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2 things are preventing boiler operation in this file.

The heating design supply air temperature is too low, resulting in zero desing load on the central heating coil.

Sizing:System,
VAV Sys 1,               !- AirLoop Name
<snip>
12.8,                    !- Central Cooling Design Supply Air Temperature {C}
16.7,                    !- Central Heating Design Supply Air Temperature {C}

The boiler water flow rate is zero, this field has no default which becomes zero. Should be autosize or a value.

Boiler:HotWater,
Boiler,                  !- Name
NaturalGas,              !- Fuel Type
10000,                   !- Nominal Capacity {W}
0.9,                     !- Nominal Thermal Efficiency
,                        !- Efficiency Curve Temperature Evaluation Variable
,                        !- Normalized Boiler Efficiency Curve Name
,                        !- Design Water Outlet Temperature {C}
,                        !- Design Water Flow Rate {m3/s}
,                        !- Minimum Part Load Ratio

Once these are fixed, you may already realize that this will supply 21C air to both zones whenever the airloop is operating. There is nothing here to link thermostat control to the system.