How to handle a business start-up expense?

Yes. Depending on the computer's cost, you may be able to treat it as an expense or as a depreciable business asset. 

You are correct in not filing for 2016. While there may well be organizational costs (the legal costs of setting up a partnership or corporation) or start-up costs (advertising, purchasing supplies, fixtures, etc.) in a prior year, a business does not start deducting those costs until the actual commencement or active trade or business.

Tip: If you are setting up the computer, or cameras and similar photography equipment as depreciable assets, use the in-service date (actual start of business) as opposed to the 2016 purchase date, when you are entering the assets into TurboTax for 2017. Otherwise, prior year depreciation, that you never were able to take on a tax return, will be assumed by the software.

For further information, please see IRS Pub. 946 How To Depreciate Property.