Target out of range is part of the connection to the server issues. It could be your connection or the server.. it's impossible to say without further information.
1. Please visit www.speedtest.net
and report back your download speeds. You say you have great internet, but I just want to be sure
2. What anti-virus and spyware protection do you use? Without proper protection, viruses and spyware can steal some if not most of your bandwidth until they are cleaned off.
3. Anyone else on your network that could be downloading files? This goes for any other programs on your computer as well. Some programs will ninja download in the background.
4. Do you run wireless or cabled internet? Cabled can help improve your connection slightly, especially with cheap wireless cards.
If all of this doesn't improve your connection some, then it could just be a bad connection to the servers.