How to monitor trafic to google servers?

It's possible for this to happen when you are using a proxy server; therefore, what I would suggest you do first is connect to Google through another internet connection to further see if it is the LAN that's actually causing this. I am still new to Wireshark as well, so I'd like to know the answer to your question as well. (:

Good Luck!

Here is what google recommends to identify the problem.

https://support.google.com/websearch/answer/86640

UPDATE

And what google recommends (installing a few malware /antivirus and scaning for malicios software) is not viable

O.K. then you need to capture the traffic in front of your internet router (LAN side). Please read the following wiki how to do that

http://wiki.wireshark.org/CaptureSetup/Ethernet#Capture_using_a_monitor_mode_of_the_switch

You will need to mirror/monitor the switch port where your internet router is connected to. If you don't have a switch with port mirroring, these are your options:

• buy a small (cheap) switch with that capabilities: http://ask.wireshark.org/questions/13892/port-mirror-switch
• try to capture packets on your internet router if it supports that
• use a PC with two interfaces in bridge mode to capture traffic in front of your internet router http://wiki.wireshark.org/CaptureSetup/Ethernet#Capture_using_a_machine-in-the-middle

As soon as you can capture traffic, you need to run that capture for some time (maybe a few minutes, maybe a few hours, maybe days - if the offending device is currently switched off).

BEWARE: You cannot simply run Wireshark for several hours/days, as your system will run out of RAM. Instead, please use dumpcap to capture only traffic to google servers (based on IP ranges). Please read the Wireshark docs to figure out how that works!

http://www.wireshark.org/docs/

Regards
Kurt