We created a C-corp about 9 years ago in Wyoming. We got an EIN number but never started the business. We didn't file any tax returns. The opportunity to start the business has now developed. Would it be simplier to request a new EIN number and "start over"?

It depends on the name associated with the EIN. Otherwise, I don’t believe there is any kind of “use” requirement for an EIN, but you need to check with the IRS. If a company is required to file a tax return, it should have an EIN number. Generally, businesses need a new EIN when their ownership or structure has changed.. You will be required to obtain a new EIN if the corporation receives a new charter from the secretary of state; you change to a partnership or a sole proprietorship.You will not be required to obtain a new EIN if you are a division of a corporation; only the corporate name or location changes.

You may want to verify the answer given below.
I'm not an attorney or CPA so this is not legal or professional advice but...
It seems there is a requirement for a C-Corp to file Tax Returns every year they are in business (exist) whether there is a profit or not. There may penalties for not having done this.