Is there a way to determine what the original source or link was for a previously downloaded file, other than using the browser's download history?
Short answer: NO.
However, sites often provide a checksum such as SHA1 or MD5 to help you verify a successful download.
You can create the checksum and then Google it. For example, I have a file:
which has SHA1 checksum:
When I Google the checksum I get the VMware Workstation 7.1 for Windows Download Page as the #1 result.
So while I can't be sure that I downloaded my copy of this file from this particular site, I can be sure that it is the same file.
It Mac OS X, it is stored in the file's metadata (right-click > Get Info). I don't have an active Windows install to check, but it may be recorded in the same way by the OS there, too (right-click > Properties). I'm not sure about that, but you could give it a try.