Hello Kevin,
Thank you for your reply.
I did everything you described exactly in that order. Must say that this computer is not mine, is a friend's who asked me to check it. I mention this because I didn't like the idea of connecting my google acct. to an infected PC using Chrome, but I did to solve the problem.
I even changed the other sync option:
Background sync
Not allowing recently closed websites finish sending and receiving data
(or somehting like that, my Chrome is in Spanish language)
Then I deleted the Google folder from Local and Roamming in %appdata%, since it was in both.
Then checked the computer with AdwCleaner, and found no infections, restarted the computer and reinstalled Google as you said.
Sadly the problem is still present. I have to say that when Chrome is not installed, no malware is found, so my suggestion for my friend would be to switch to Firefox, since in my experience it is more stable and reliable.
I contacted Google about the problem but have not get any reply yet (just contacted them about 1 hour ago).
Now, I hope the virus is not in my own Google acctount since it got linked with the infected google Chrome