Edit: Mike beat me to it ;-)
Certain page layouts will hide the Quick Launch. This isn't just related to publishing features, but the type of layout you're using. Certain web part pages, welcome pages, etc. will hide the quick launch. Usually they hide it with some simple CSS, so you should be able to re-enable it.
<style type="text/css">
/* hide quick launch */
#s4-leftpanel {
display: none;
}
.s4-ca {
margin-left: 0px;
}
</style>
<style type="text/css">
/* show quick launch */
#s4-leftpanel {
display: block;
}
.s4-ca {
margin-left: 155px;
}
</style>
UPDATE:
I ran though this in my lab to duplicate your scenario. It turns out that the Welcome Page page layout uses a more specific CSS selector, so you have to use that same selector if you're going to reverse the action and show the left panel.
If you go to a page using the welcome page and view your source (assuming you're using the OOTB master), you'll see a CSS block directly before the <link rel="shortcut icon">
tag that looks like the following. This is the markup that the welcome page layout is using to hide the left panel:
<style type="text/css">
.v4master #s4-leftpanel { display: none; }
.v4master .s4-ca { margin-left: 0px; }
</style>
Given that the CSS selectors are prefixed with ".v4master", you also need to use that prefix in your overwrite markup, so you would need to use the following (updated from my original solution above):
<style type="text/css">
.v4master #s4-leftpanel {
display: block;
}
.v4master .s4-ca {
margin-left: 155px;
}
</style>
I have tested this, and it does work. In my test I simply added that markup to a Content Editor Web Part on the welcome page and it turned the left panel back on and everything behaves like it wasn't turned off by the page layout in the first place. Obviously you have to do it to every page that uses that layout if you really want it everywhere. The smart thing would be to create a text file that has the markup in it, upload that to your site, then point the CEWP's to that file, so you have a central place to change it in the future.