Help me determine if my Linux server is blocked by another

I have a Java app that checks the status of documents on other servers. It works fine except for a couple of servers don't respond, but when I check from my local computer they respond fine, so I need to determine if they are not responding to my server for some reason, or if there is something else going on. This project is to help me determine if my server is being blocked. I think the best way is to use Lynx to try to access the document on the remote server from my server, but you might know a better way. This will probably take less than an hour. I have full root access to my server, but of course can not give that out to anyone, so we will have to use TeamViewer (free) so that you can gain access to the server from a connection to my desktop. This needs to be done in the next few hours, so please only bid if you can be available today.