"Cannot connect to the real Gmail.com"
Solution 1:
Looks like Chrome doesn't appreciate what your ESET security software is trying to do (i.e., MITM'ing its connection).
You might try disabling ESET's SSL scanning.
If you're not running ESET, then you have more serious problems...
Solution 2:
Check your system time - could be incorrect
Once the time is changed (assuming it was incorrect), type "proceed" (no quotes) directly in the browser window (so you won't see what you typed).