Adobe Reader web file damaged and could not be repaired

This sounds like the file gets damaged in transit. Have you tried to download the file to your disk, and then open it from there? Does it open once it's a local file?

Yes, I've tried that and it still comes up damaged.  Yet when I pull it up from outside our network it opens fine.  And not all the pdf's display this error from the web site.

This means that something gets corrupted when the file is transmitted. What web server are you using?
PDF is a binary format. Sometimes software ignores that fact and treats PDF files as text files and messes around with line endings, or certain characters. This will corrupt a PDF file. Sometimes the corruption is not severe enough, and Acrobat can repair the file (you usually see a popup for a split second when you open the file), but in most cases, you will end up with the error message you see.
To force software that can recognize binary files to do so, there is usually a comment on the second line in the PDF file containing binary data.

Nothing you can do in Acrobat or Reader will fix this problem, you need to change the way the file gets send on the server.

Change the way the file gets send on the server?  Ii believe you mean saved on the server....how would we do that if we can't even access it?  We have tried to download and save to the desktop, but when we open it from there we recieve the same error.

You said that when you access the file from outside your network, it opens. This means that it's not how it's saved on the server, it's how the server sends it to the browser (or something in between). You need to talk to your server support people to find out why the server is behaving differently between an internal vs. an external request.  

This is a pdf on someone elses website.  So from by laptop at home I can access the website and open the pdf file.  But when I'm at work I can access the web site but the pdf's fail.  From your message it sounds like you were under the impression that this was our website?

Yes I was under that impression. In that case, check your firewall/proxy (I assume you are using a proxy to access web content from within your company).

Yes we use a proxy.  I did find the content size was too low to open these attachements.  But that did not resolve the problem.  I'll monitor the logs to see if I can find what is causing it.  If you have any suggestions on what to look for please let me know.

Can you download one of these files from outside, and the same one from inside our network. Then Compare the two. Is one chopped off? Do certain characters not show up correctly in the corrupt version? Keep in mind that PDF is a binary file format, and it may not be easy to compare the two files, but I think this is the only way to figure out what is different, and then we can tackle the "why?"

I compared the two pdf's (same pdf), one pulled outside of network and the one pulled inside the network, in notepad and the one from inside the network contains only about a quarter of the script.  So it looks like you are correct in that it is being chopped off.  Of the text that did make it, it looks identical to the good pdf.

I found what was causing the problem.  The firewall HTTP proxy was denying the message due to a signature ID found on the web page that was being blocked.  I added the signiture to the acceptable ID's and that resolved the problem.