Why in a voltage driven parallel RLC circuit (at resonance), the current of the inductor has a DC component?
Just so we are on the same page... You have your resonant tank (which might be closer to 159155Hz) in parallel with a resistor of \$100\Omega\$. That pretty much means \$\infty\$ for the tank, leaving the \$100\Omega\$ resistor. So the DC current from the source isn't surprising. Removing the resistor just leaves the tank. But since it is \$\infty\Omega\$ at resonance, again it is no surprise that there is then zero DC current. I'm guessing that you already know this stuff. The only reason I'm bringing it up is to make it clear that we both see the same thing here.

So... You are probably using the transient analysis and not allowing enough time to go by. Have you considered running the analysis for, say, 5ms? (The time delay will need to be about the same with and without the resistor.)