Please, don't fall on these idiots stories about bios hacks. Why would someone hack your BIOS just to show ads? Come on.
Your computer isn't infected. If you have no problems without your Google account logged, then it is a problem.
If it's not in the Bios then what can it be? I formatted my secondary Hdd (im still on windows 10, I just tested the other and replaced with after the test) installed windows 7, problem began without me even login in to my Chrome account. So at this point I don't think it's the account. If I do have something, it's either Bios or it hides itself well from programs that remove malware. But that's just my opinion and I'm no expert. What can be happening here in this specific case? A brand new install of Windows 7 that I made in a hard drive, no signing in on my account and there it was, default browser causing problems again.