Looks like there is some problem with your Machine. You should be able to ping smtp.gmail.com
Is it a server (Company Machine) or just a test box at home ?
If it is a server, contact your network team, I faced same issue while configuring database mail at my company. I then requested my Securty team to unblock port 25 and then asked my Notes team to add my server name in smtp server list.
If it is a Test box, try SQLMail using Outlook. If outlook does not works they definitely Database Mail wont work.
Also Check if is_broker_enabled = 1 for msdb.
Database Mail uses this feature.
You said you have disabled Firewall and AV while testing ? So ports blocking should not be an issue.
I still wonder why you are not able to ping smtp.gmail.com ?