Do you have an auto-updater or some other process (virus scan, etc.) scheduled to run during that time frame? If so the Internet share or additional resource useage might be causing this.
If you don't have anything scheduled, try running a virus and spyware scan. Maybe you're infected and the infection has schedled itself to try to communicate out.
I have run the virus and spyware scan and everything is ok. My virus program is schedule to run in the mornings, and in the past my virus program hasn't caused any problems. Using AVG and spybot. I also have a registry cleaner and junk something or other cleaner, so I don't think the problem is there.
I do think the problem is internet, so if it continues, I'll run the ping plotter and see if someone can tell me something. I have no idea what all that stuff means.
Thanks for the suggestions.