Specific Wine Applications don't have Internet Access
Solution 1:
There is a solution suggested in this post: How to configure wine to install Evernote?, explained further here: instalar-evernote-en-linux (is in Spanish but it has a lot of images)
You could install playonlinux. Once PlayOnLinux is installed, goto manage wine versions, and install wine 1.4.1 32bit.
Then click install program -> install a non-listed program -> Install a program in a new virtual drive.
Give a name for your application virtual drive ("evernote" or whatever you like), then mark Use another version of wine and select the 1.4.1 that you've just installed. Kind of virtual drive I choose 32bit windows installation.
Browse for the installer in your drive, wait for the installation to finish and close Evernote, so PlayOnLinux can notice that the installation has finished.
This works for Evernote_5.8.13.8152 in Ubuntu 15.04.
Solution 2:
You need the 32 bit dns resolution libraries. To install this library, run one of the following commands as root:
64-bit Debian 8 : apt-get install libnss-mdns:i386
32-bit Debian or Ubuntu : apt-get install libnss-mdns
64-bit Ubuntu : apt-get install libnss-mdns:i386
32/64-bit Fedora : dnf install nss-mdns.i686
32-bit Mandriva : urpmi nss_mdns
64-bit Mandriva : Not available
32-bit SUSE : zypper install nss-mdns
64-bit SUSE : zypper install nss-mdns-32bit
32-bit Arch : pacman -Syu nss-mdns
64-bit Debian 7 and older : apt-get install lib32nss-mdns
Nothing but wine needs 32 bit binaries as it is mentioned here: https://wiki.winehq.org/FAQ#Why_doesn.27t_DNS_resolve_in_64-bit_operating_systems.3F