Ask HN: Is filing federal forms necessary for shutting down idle C-Corp?

I am looking to dissolve a Delaware C-Corporation - and I have been advised to file a final Form 1120 as well as a Form 966 with the IRS. Are these really necessary if the business did nothing the previous year? No sales or income, etc. What are the penalties for not doing so?

If I choose to do file the "zero return" etc, how do I even do it? Print out the form and send it in to the IRS? I cannot find out how to e-file easily, for instance.

I do plan on dissolving the business with the State of Delaware anyway, and would like to button things up to a reasonable level - and would like to avoid spending thousands of dollars and/or spending more than a few hours.

Any resources, tips, advice, or links that can be shared are appreciated!