Unless exempt under section 501, all domestic corporations (including corporations in bankruptcy) must file an income tax return whether or not they have taxable income. That would mean your C corp would be required to file an income tax return for its fiscal year.
Intuit offers a product, TurboTax Business, that can be used to prepare an income tax return for a C corporation (Form 1120). Note that TurboTax Business is not available as an online product nor will it run natively on a Mac; it must be installed and run in a Windows environment.
Regardless of the foregoing, it is strongly advised to seek professional guidance and have the corporation's income tax return prepared by a tax professional (or at least reviewed after you prepare the return).
You do have to file C-corporation tax return.
Per IRS and their Corporations instructions: "Unless exempt under section 501 of the Internal Revenue Code, all domestic corporations in existence for any part of a tax year (including corporations in bankruptcy) must file an income tax return whether or not they have taxable income."
The corporate returns, such as C-Corp (Form 1120) can be filed using our Turbo Tax Business package: