Hi There,
System Restore if is not working for a particular date then you can go back to earlier dates and try to do a system restore once again.
About "Invalid handle messages from my external modem braodband stick error 6."
Navigate to Device Manager and go to Network Adapters and uninstall the current driver for Network Adapter and restart the computer. Once the computer restart the computer will install the new drivers for Network Adapter.
Let me know if it works.
Thanks