Of course you can start some kinds of businesses with no capital. Service businesses tend to need a lot less capital than product businesses. Professional service businesses such as graphic arts, management consulting, engineering consulting, accounting and similar businesses don't need a lot of capital.
If you have clients -- as in work to do and clients to bill for it -- you can get going very fast.
I'm not an electrical engineer, but I have to assume you can start your own business as an electrical engineer for hire, as a consultant, without needing much more than your expertise and credentials. Will your business require equipment such as a computer? Will you need a marketing budget? You might, but then again you might be able to start your consulting business simply by calling a few contacts and getting hired.
Also, put yourself on Facebook, LinkedIn, and Twitter, if you haven't already. Those are all free avenues for finding customers.
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Question added to topic Franchises • April 25, 2011
Can I Start a Business with No Startup Capital?
I am an electrical engineer and want to be my own boss. But how can I start a business if I have zero capital to work with?