I am currently on L2 visa (valid till 2015) in US and I am planning to start a small business with my EAD which is valid till 2014
Yes, but you can only work while in possession of a valid EAD.
You should retain an experienced immigration lawyer, whether myself or one of my colleagues, to review all the facts, advise you, and handle the case.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
I believe this is a repeat question - I mentioned an E-2 for you, but as this question is phrased a little differently - the answer is yes you can as long as the EAD is valid.