I am an inventor. I belive I have designed a new gasoline engine. My
question is: Where can I look for a grant (research and development
funds) to meet the patent (about $8000) and the prototyping expenses
(about $200,000).

Hi

Apart from the obvious answer of involving investors, there is a large
site which primarily deals with enery conservation inventions, but if
you scroll down the page found at
http://www.energy.state.or.us/bus/invent.htm you will see that there
are several National Resources which you might find relevant.

These are helpful as they show the various values of the grant awards
available. You have not stated whether the new engine you have
invented offers anything towards conservation of fuel economy or/and
environmental improvement over existing gasoline engines. If it does,
there is more chance of getting a grant from the many associations
that are listed there.

You may also find this site http://www.ala.org/acrl/resjuly99.html
useful as it has very helpful starter hints on where to start when
looking for funding for a new invention. However, some of the links I
did find were out of date, whereas others are thankfully functional.

I appreciate that until the engine is patented you would (as would I) 
be reluctant to divulge too much information so with only limited
information as to the functionality, it is hard to say who is most
likely to be interested in such an invention to provide funding for
the same.

However, the above sites that i have listed should give you a good
starting point with many avenues to explore to get you closer to your
goal.

I wish you the best of luck. I'll look out for the jabajab engine.

Excellent answer, clear, useful, meeting exactly my need, and with
pleasant personal touch.