I have a very specific idea for a piece of computer hardware that I believe would be very useful. I do not have a prototype, nor do I even know how I would create such a prototype. I would be willing to join a company who manufactures this sort of hardware and work to realize its development. I would also be willing to exchange the rights to the idea for either employment, money, shares or licensing. I do not have a patent (in part because I do not have a prototype) and I have performed a cursory search to see if this concept has been created.

You do not need a prototype to patent your idea, my friend. Read the link below. I also inlcluded another link that tells you when you should or should not get a patent (to prevent you from getting scammed by "Patent Corporations.") from a Patent Corporation.
However I would recommend either applying yourself or hiring a lawyer.

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The third link is to the FAQ of the US Government Patent Office. You would be applying for a Utility Patent, which is the one used for Machines and most other invention types.

The next link is a link to a form called Declaration For Utility Or Design Patent. This is the form you would fill out if you wanted to patent the idea yourself, they recommend getting a Patent Attorney, but I see no problem with doing it yourself as long as you study up on uspto.gov website a bit.

In that case you would use our fifth and final link, which is the one you fill out if you wish to patent with the assistance of a Patent Attorney.

Good luck. :)

EDITED POST – Also discovered a clear and concise page detailing who is eligible for what. http://www.uspto.gov/web/patents/howtopat.htm