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How can I estimate business taxes / filing fees for a business that has $0 income?
You need to hire a tax professional and have them sort it out for you properly and advise you on how to proceed next. Don't do it yourself, you're way past the stage when you could. You're out of compliance, and you're right - there are penalties that a professional might know how to mitigate, and maybe even negotiate a waiver with the IRS, depending on the circumstances of the case. Be careful of answers like "you don't need to pay anything" that are based on nothing of facts. Based on what you said in the question and in the comments, it actually sounds like you do have to pay something, and you're in trouble with the IRS already. It might be that you misunderstood something in the past (e.g.: you said the business had filed taxes before, but in fact that might never happened and you're confusing "business filed taxes" with "I filed schedule C") or it might be the actual factual representation of things (you did in fact filed a tax return for your business with the IRS, either form 1120 of some kind or 1065). In any case a good licensed (CPA or EA) professional will help you sort it out and educate you on what you need to do in the future.