Do I have to file back taxes on my inactive corporation?

Even if your corporation earned no income, many states have what they call "minimum franchise taxes." This is like an annual fee/tax for the privilege of being able to say you are an incorporated entity in the state.

There are also reporting requirements, like filing annual taxes -- again, even if just to show that you did no business. Once formed, a corporation has ongoing maintenance requirements even if you're out of state and not using it. Speak to a local accountant familiar with business issues to see if there's a way to streamline the tax filing process (in light of the lack of activity) and to avoid any penalties and interest that might have accrued.