How to start a new list, continuing the numbering from the previous list?

Solution 1:

A much easier solution to the OP's problem is the following:

<ol start="X">

Where X is the value of the list you want to continue, so in his sample:

<ol>
  <li>You can't touch this</li>
  <li>You can't touch this</li>
</ol>
<p>STOP! Hammer time.</p>
<ol start="3">
  <li>You can't touch this</li>
</ol>

Solution 2:

As already said, you need :before and content, but you also need to disable the default list numbering. This is your fixed CSS:

ol.start { 
    counter-reset: mycounter; 
}
ol.start li, ol.continue li {
    list-style: none;
}
ol.start li:before, ol.continue li:before { 
    content: counter(mycounter) ". "; 
    counter-increment: mycounter;
}

You don't need to reset the counter for ol.continue, just continue to use your custom counter. The above code makes sure that the counter is only used for the ol.start and ol.continue lists.