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.
Very often a virus will prevent SR from working, be sure you are clean. Make a complete anti virus scan. Download and make a full scan with Malwarebytes. Be sure to get the free version. http://www.malwarebytes.org/
In addition, try in safe mode, and try with your antivirus turned off.
Norton in particular can cause this problem.
The Windows System restore can be very buggy. Many reasons can prevent it from running properly. One frequent cause of irouble is the AV program.
For a test I suggest you disable your AV program and try again.
In the future, you might want to use Imaging for your protection. That is a lot more reliable. Free Macrium or free Paragon are good programs to use. Here is an example that works for XP, Vista and Windows7 - all the same: Imaging with free Macrium - Windows 7 Forums