Yes, you can. But you can't form an S-Corporation. For that you have to be a citizen of USA. There are multiple ways of starting your own company, but one of the most effective one is by incorporating
"Limited Liability Company" ( LLC ). You can find lots of companies on the net which can do this. They may charge you around 150-200$, and the procedure may take few days. LLC can be a "Partnership Firm" or the liability protection as a "Incorporated Company". You can be the Chairman or Director of the board, but you can't work for it, unless you have an H1 visa issued from that company. But, you can always hire a CEO for the company, who has a work permit (Green card or Citizen etc.). For more information about LLC's visit: http://www.llc-usa.com

(Source:http://www.path2usa.com/immigration/h1bcorner/h1b_tips.htm)

Can a nonimmigrant, foreign worker invest money in any venture?

A foreign national who is living or working in the United States can invest money in any venture or enterprise. The law allows foreign nationals in the United States to purchase any assets or property, including real estate. Conversely, in order to protect U.S. workers, both citizens and green card holders, the United States Citizenship and Immigration Services (USCIS) and the U.S. Department of Labor (DOL) require that the foreign national obtain certain work authorization.

In other words, a person on an H1B or other temporary work visa in the United States is legally allowed to invest in any venture or company and could possibly undertake some limited volunteer work on behalf of the venture or company. However, the individual cannot work indefinitely for that company and earn a salary without obtaining prior approval from the USCIS or DOL to work for the particular venture or company.

(Source:http://www.murthy.com/startup.html)