You don’t say who “we” are who are scrambling or how you are on the board if the “whole board” walked out.  Assuming that you and perhaps a few others are still members of the board, you probably have the power under the bylaws or the state nonprofit corporation law to fill vacancies on the board.  If the organization has voting members, the voting members can probably also call a special meeting to elect new directors if no other process is spelled out in the bylaws.

You (i.e. whoever is involved in re-establishing the governance of the organization) should first assure that those who walked out actually resigned from the board and won’t claim that they merely ended the meeting abruptly.  You don’t want the walkers to try to get back in the game when you start to do things.

When you determine how many vacancies you actually have as the result of the walk out, you should then use whatever process is available to fill those vacancies (and perhaps more if you had additional unfilled positions under your bylaws).  Your newly rejuvenated board can then undertake an investigation of the alleged sexual harassment and sales of museum items to see if any further action is required.

You don’t have to find solutions to all of these issues alone.  You will have fulfilled your immediate duty if you merely start the process to reestablish a working board.  The board can then figure out what should be done going forward.