How can I determine the collector voltage of Q1 in this circuit?
The real world answer to..

"What is the collector voltage with respect to ground, is it zero, or 15V?" 

is NEITHER!

The model below is what you really have for DC.







simulate this circuit &ndash; Schematic created using CircuitLab

Real world components and the PCB, wiring etc. have intrinsic and parasitic resistances and capacitances. As such, in reality, your model looks more complicated.

As you can see, there is a resistor divider in there between the leakage resistance of the capacitor and the leakage resistance of the transistor (Which includes the parasitic resistance of the build). There is also a capacitor divider between the capacitor itself and the junction capacitances of the transistor and wiring, C_OFF.

As such the final voltage will be set by that resistor divider. 

When you first power the circuit the collector voltage will be dictated by the capacitor divider then decay to the resistor divider voltage. How long it takes to reach that voltage will be dictated by the sizes of those resistances and capacitances.  

Note, there are also numerous inductances not shown in the above model that complicate matters even more.

Interestingly it is actually very hard to measure this. Since the values involved are usually very large resistances and very small capacitances, attaching pretty much any measuring equipment disturbs the balance significantly.