Finding the energy over the capacitor in DC
I'll provide a simplification of the schematic to get you started:







simulate this circuit &ndash; Schematic created using CircuitLab

Note that there is no possible need to worry about where one end of VCCS1 is connected. In your schematic, one end is tied to \$+12\:\text{V}\$. But that's irrelevant. So it's better to just leave it unconnected so you don't get confused about dealing with something that isn't relevant to the problem.

Now, you can see that I've also Thevenized your resistor divider to make things somewhat simpler. In fact, it's now so simple that you can solve it for the steady state VO (at \$t=+\infty\$) very quickly.

Of course, this also assumes that once you have VO that you know how to compute the capacitor energy from it. But the equation is everywhere, so I don't mind including it here for convenience:

$$w=\frac12 C V^2$$

As you can see, the voltage is squared here so both positive and negative voltage values will produce positive energy values (assuming the capacitance is also positively-valued, of course!)