What date would I use as start date for S-corp if we haven't conducted any business yet? We are still building an eCommerce website that has not bought or sold anything.

Your "start date" can be either the date you incorporated or the date when you first report either income or expenses on your tax return (Form 1120-S). 

You are not required to file a business tax return until you have business income and/or  business expenses, deductions or tax credits.