If you are able to boot in safe mode with networking, try installing malware bytes as aford recommends, update it, scan the whole system.
Put the Norton disk in the drive and start the computer, the norton disk may scan without starting windows. It's surely worth a try. Make sure the internet is plugged in when you do this.
If both those fail to find malware, back up your files to a CD, DVD, or online backup service such as Mozilla, or a thumb drive, whichever works.
Reformat the drive and re install the operating system. Then reinstall your backed up files.
Unfortunately, it sounds like a virus infection, which you may not be able to get rid of without reformatting the drive.