Depending on your theme, applying BP Template Pack may end up placing the sidebar and content wrappers at the same level than the header and the footer:
<div id="wrapper">
<div id="header">...</div>
<div id="content">...</div>
<div id="sidebar">...</div>
<div id="footer">...</div>
</div>
But you need them to be inside their own container. BP uses something like this:
<div id="header">...</div>
<div id="container">...</div>
<div id="content">...</div>
<div id="sidebar" role="complementary">...</div>
<div id="footer">...</div>
Your theme is probably using a different structure and/or container names from BP, for example:
<div id="wrapper">
<div id="header">...</div>
<div id="content">...</div>
<div id="main">...</div>
<div id="sidebar" class="col-right">...</div>
<div id="footer">...</div>
</div>
or something like that. You need to check the structure of your theme in a page where your sidebar is displayed correctly, and then modify the template files BPTP copied to your theme to reflect that structure.