Judging from the definition of these visa categories, H1-B is issued for a
particular job, at a specific company. IMHO, the logical extension of this
definition is that you cannot work at another company (even your own
start-up) unless you have specific permission (another H1-B ?) to do so.
Again, by definition, H-4 visa holders *cannot* engage in any professional
activity.
Interestingly, this goal may be reached via the L-1 route; but, I believe
one of L-1's requirements is that the individual *must* have been employed
in a managerial or executive capacity, for a minimum of 12 months within
one of the three preceding years by the overseas affiliate.
I am sure you have considered consulting an immigration attorney, who would
be best qualified to answer these questions. In fact, these are questions
that have most likely been answered in FAQs at lawyers' websites such as
www.murthy.com, www.visalaw.com, www.greencard1.com etc.
Regards,
Tushar.
p.s. The usual disclaimers apply.