The code within your NAV element is invalid HTML.
You have this which is just all sorts of wrong:
<table>
<ul>
<tr>
<td><li><a href="BTSMain.html"><b>Home</b> </a></li></td>
</tr>
<tr>
<td> <li><a href="BTSServices.html"><b>Services We Offer</b></a></li>
</td>
</tr>
<tr>
<td>
<li><a href="BTSAboutUs.html"><b>About Our Company</b></a></li>
</td>
</tr>
<tr>
<td>
<li><a href="BTSTestPage.html"><b>Testing Page</b></a></li>
</td>
</tr>
<tr><td><li><a href="BTSTestPage2.html"><b>Testing Page 2</b></a></li></td></tr>
</ul>
</table>
Try changing it to this:
<nav>
<ul>
<li><a href="BTSMain.html">Home</a></li>
<li><a href="BTSServices.html">Services We Offer</a></li>
<li><a href="BTSAboutUs.html">About Our Company</a></li>
<li><a href="BTSTestPage.html">Testing Page</a></li>
<li><a href="BTSTestPage2.html">Testing Page 2</a></li>
</ul>
</nav>
The reason your NAV element is moving out of place when you add a border will probably be because adding the border gives the NAV element a larger width.
e.g if your NAV element is 300px wide and you give it a border of 1px that will make the NAv element 302px.
Read up on the HTML Box Model to understand this better.