Once I used NetHandle all seems to be working perfectly. Thank you dsiders.
NetHandle := InternetOpen('Mozilla/5.0(compatible; WinInet)',
INTERNET_OPEN_TYPE_PRECONFIG, nil, nil, 0);
dwTimeOut := 5000; // Timeout in milliseconds, so 5 sec.
// InternetSetOption(IntPtr.zero, INTERNET_OPTION_CONNECT_TIMEOUT,
InternetSetOption(NetHandle, INTERNET_OPTION_CONNECT_TIMEOUT,
@dwTimeOut, SizeOf(dwTimeOut));