Simple elapsed time counter
Remarks to your code


Function names should be using camelCase.
Two minor formatting errors: function ElapsedTime (), if(oDiff).
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You mentioned ES6 in your question, so: var nTotalDiff could be declared using let and var oDiff using const.
You declare oDiff in TimePassed() as a global variable (you forgot var).
oDiff.seconds is declared, but never used.
(new Date()) can be written as new Date().
Specifying 1491685200 in human readable format would be better, I think.Update: suggestion removed due to the problem pointed out in the comment to this answer.
If you leverage power of modulo operator, you can get rid of all these nTotalDiff -= oDiff.██████ * ███.
alert(oDiff.days + 'd ' + oDiff.hours + 'h ' + oDiff.minutes + 'm ') can be written in ES6 using template literals as alert(`${oDiff.days}d ${oDiff.hours}h ${oDiff.minutes}m `), although space after m is unnecessary whatsoever.
Having two functions named ElapsedTime() and TimePassed() seem ambiguous.
Your code is not in strict mode.


My rewrite



const elapsedTime = () =&gt; {
  'use strict';
  const since   = 1491685200000, // Saturday, 08-Apr-17 21:00:00 UTC
        elapsed = (new Date().getTime() - since) / 1000;

  if (elapsed &gt;= 0) {
    const diff = {};

    diff.days    = Math.floor(elapsed / 86400);
    diff.hours   = Math.floor(elapsed / 3600 % 24);
    diff.minutes = Math.floor(elapsed / 60 % 60);
    diff.seconds = Math.floor(elapsed % 60);

    let message = `Over ${diff.days}d ${diff.hours}h ${diff.minutes}m ${diff.seconds}s.`;
    message = message.replace(/(?:0. )+/, '');
    alert(message);
  }
  else {
    alert('Elapsed time lesser than 0, i.e. specified datetime is still in the future.');
  }
};

document.getElementById('counter').addEventListener('click', elapsedTime, false);
&lt;button id="counter"&gt;Check elapsed time&lt;/button&gt;




Remarks


/(?:0. )+/ matches sequences of one or more zero followed by any character and a space. It is used to change potential output that would look like 0d 0h 0m 1s to simply 1s.
In message I added word over, because the calculated time is in fact the least amount of time that could have passed (calculation time, Math.floor(), instantaneous nature of time specification invalidation).