Gmail is not linked to your BIOS, Windows User Account or the Teredo tunnel AT ALL.
Change your Gmail account password, change the password to the account that you've set as the backup/recovery account and that should go a long way towards resolving your issues.
Teredo tunneling comes by default on modern Windows operating systems, it is not malware, some security implications are related to it, but in itself it's not a virus. It effectively acts as a bridge so IPv6 can talk to IPv4 etc.
If you're concerned, type the following into command prompt to disable teredo tunneling:
netsh interface teredo set state disable
If you start to experience network connectivity issues (cannot connect to certain sites etc) then you can re-enable it using this command:
netsh interface teredo set state enable
Athlon II x4 645 || 1TB 7200rpm HDD || EVGA GTX 650Ti OC || 8GB DDR3 RAM || Windows 7 Home x64
i5 4210M || 500GB Samsung EVO 850 SSD || GeForce 825M || 16GB DDR3 RAM || Windows 10 x64