Now, there are very few things that irk me more than someone who complains but never offers a solution, so this post is proof that there is indeed a solution (and indeed a very simple one) to this problem.
To test it, I downloaded this file, hashed it, and got an MD5 of 0D01ADB7275BB516AED8DC274505D1F5. I downloaded about half the file, paused it in firefox, renamed the .pdf.part file to .pdf, resumed the download, hashed it, and got 0D01ADB7275BB516AED8DC274505D1F5. The file resumed exactly as I expected it to.
I threw together a quick download resumer and I've posted the project if you want the whole thing. Otherwise, these 4 lines contain the one line where the "magic" happens:
// create the requestCalling request.AddRange creates the header "Range: bytes=n-" where n is the number of bytes remaining in the download. Using this, browsers can append the desired bytes to abandoned file starting at exactly the position it left off. They could support it natively without plugins and allow you to "attempt to resume and hope for the best."
HttpWebRequest request = HttpWebRequest.Create(Source) as HttpWebRequest;
request.Method = "get";
// set the range
// get the response . . . a.k.a., the "magic"
response = request.GetResponse() as HttpWebResponse;