Hi,
I use both linux mint 18.1 sarah and ubuntu 16.04 as dual boot into my same pc. I was able to get connected via DSL broadband internet connection into both linux mint and ubuntu. But few days ago, I noticed that linux mint can no longer detect DSL wire connection. But ubuntu is ok.

What is the cause for this problem? more information needed? which information do you need?

There are two (sometimes 3) stages in activating a network card.
1) The kernel detects the card and loads the correct driver. At this point a device name is created.
1.5) Some wireless cards load firmware here, but I've never heard of a wired card needing any firmware.
2) The device gets an ip address, usually from the router via dhcp.

Since the card works in Ubuntu, we can exclude problems such as bad wiring or failure of the router to reach your isp's server.

I suggest you first check for the network device using /sbin/ifconfig. It will probably be called something like enp0s25, but it might still have the traditional name eth0. If it isn't there, you have a kernel problem. If it is there but has no address, there's something wrong with the network boot script.

Just out of curiosity, what else changed a few days ago? Did you update dhcp?

Hello and welcome to LQ.

Best part of this is that it did work at one time.

Ideas also.

lspci or lsusb for the nic.

ifconfig command

Use your connection manager to see what the settings are.

What caused it? Since Ubuntu works we'd have to that that some change to Mint did it. What that change could be is either settings, driver support or some oddity the hardware.