I am preparing taxes for my inactive S-corp just now with zero activities and just realized that that the the March 15 deadline for extension has past. What do I do now?

You can still e-file your 1120S return, and there's nothing special for you to do to ensure that. But because it is late, you will be subject to a late filing penalty. There's no exception for an S-Corp that had no business activity for the year. When S corporations fail to file Form 1120S by the due date or by the extended due date, the IRS will impose a minimum penalty of $195 for each month or part of the month the return is late multiplied by the number of shareholders. See this link to a discussion of S-Corp Filing Dates.