The cause of the exception is that you aren't receiving any items in the response. Therefore, Single will throw an exception. To avoid the exception, you can use SingleOrDefault and then check the results for null before trying to use it.
While that removes the cause of the exception, it won't help fix your other problem, related to your firewall. I mentioned port 443 in case it's blocked by the firewall, but that still sounds unlikely because how would you ever use SSL - I mention it anyway
in case it might help.
Just to let you know, there shouldn't be any inherent difficulty with a firewall, as long as it allows normal Web traffic and communication with Twitter. I'm not sure what to do, except share ideas until something starts working. Here are a couple ideas:
1. Download the LINQ to Twitter source code and run one of the demos that are similar to what you're trying to do, both inside and outside the firewall. The LinqToTwitterDemo project has working code and we'll know more after running that.
2. If that doesn't work, download Fiddler2 and watch the traffic request and response for the API you're having trouble with. The responses are in JSON and you can find a free JSON formatter on-line that will make it more readable if the response is large.
Look at response headers to see if they provide information. You might have to configure decryption in Fiddler2 to see the results, but there's help on the download site. This is a great tool that I use all the time, so you might want to get it anyway to
help debug future problems, using this as an excellent way to learn how to use it.
Before posting anything, make sure you sanitize your OAuth headers so you don't accidentally share your credentials.