New Small Business Quarterly Tax

What kind of business? This really matters. Sole proprietorship? Single Member LLC? Partnership? Multi-member LLC? S-Corp? C-Corp? Something else? It would also help to know what state, because state laws for different business types do differ among states.Those laws can also differ among jurisdictions within a state too. 

But at the federal level, you have nothing to report to the IRS until you are officially "Open for business". That may not be true at the state level, depending on the state. Now I would expect that since you filed a "no activity" report with whatever state you're in, that tells me two things.

1) Your state taxes personal income. (May not be so, depending on the type of business.)

2) You are not officially "open for business" yet. 

So based on my assumptions, any business related expenses incurred prior to the official open date, are what's referred to as start up expenses. Those startup expenses are deductible in the first tax year you are actually open for business. It doesn't matter in what year those expenses were incurred either. Basically, for startup expenses you can deduct a maximum of $5000 of those expenses in your first year open for business. But that only makes sense if you actually have the taxable business income to deduct them from. Then anything over that is amortized (not capitalized) and deducted (not depreciated) over the next 15 years. 

Now all this assumes your business type is a sole proprietorship or single member LLC.  Additionally, it would appear your state considers you "Open" as of the date your registered the business with the state. So if you really weren't open for the first quarter, then having filed the "no activity" statement with the state, means you're all done with your first quarter state requirements.