Windows SharePoint Search Access Denied

This is a re-post in order to make the solution to this error more transparent.  The problem was that our SharePoint Search service was not returning any results. I found the following event occuring in the Event Viewer.

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Event details:
Event Source: Windows SharePoint Services 3 Search
Event Category: Gatherer 
Event ID: 2436
Description:
The start address cannot be crawled.
Context: Application 'Search index file on the search server', Catalog 'Search'
Details:
Access is denied. Verify that either the Default Content Access Account has access to this repository, or add a crawl rule to crawl this repository. If the repository being crawled is a SharePoint repository, verify that the account you are using has "Full Read" permissions on the SharePoint Web Application being crawled.   (0x80041205)
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This stumped me for a long while until I finally took the time to dig in and do the proper research.  I found another error showing in the SharePoint log file:

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CSTS3Accessor::GetDocFormat: Return error to caller, hr=8007007A - File:d:\office\source\search\search\gather\protocols\sts3\sts3acc.cxx Line:654
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A simple Google search turned up this post by Yorick with the solution.

Thanks Yorick.