Sounds like your getting end-to-end communications which a good sign, but are not able to manage multiple connections.
This should be an easy fix if you have a non-propriatary network.
First go into your Network Connections then Right Click on the device icon that access the internet you will notice that you have a menu window that pops up. Now look for the properties and click it. Doing this will bring up a window the "Local Area Connection Properties" window. In this window you should notice a QoS Packet Scheduler that should have a check box to its left. If this check box is un-checked, go ahead and place a check box in it. Save your settings by clicking "ok" or "apply" which ever one is their. For good measure, go ahead and re-boot your machine. Once your logged back in attempt to access the internet multiple times.
Good luck.