I see I wasn't real clear in my first response... sorry.
Let's try this again..
Don't try to move shortcuts or open program buttons, they won't be dragged.
There are a total of only 2 bars enclosing the quick launch.
One is directly next to the Start button, the other at the far right of the last quick launch icons, normally.
One bar is assigned by Windows to be on the left side of the quicklaunch icons the other is the right side. If they get reversed, the quicklaunch icons will be on the wrong side and the open program buttons will be next to the start button.
If the quick launch is not set wide enough, there will be a type of chevron symbol there to indicate some are not exposed, and this is not usually a problem as it can be slid over to the right a bit more after it is located on the same taskbar as the start button (single height), again, this is when it is normal.
Now, to adjust....
If the right side vertical bar is misplaced, the taskbar remains double thick. Sometimes it will be at the far left under the left vertical quick-launch bar near the Start button, they are one over the other. Grab just the lower bar and drag it to the upper bar and be dragging it to the right a bit.
The open program buttons may suddenly be on the wrong side of the quicklaunch shortcuts, but, all quicklaunch icons and open program buttons are on the same plane. If this happens, grab the top, left bar and drag it to the right and down to the bottom of the double-high taskbar to flip.
Let go of the mouse button when they switch places so the quicklaunch icons are on the left of the open program buttons.
This whole process is about getting the quicklaunch bars on the same plane and in the right order. Sometimes a bar may be double-high, but originated on the bottom while the other bar is also double-high but originated on the top. If you play with it a bit you'll find out who is who and where they really are from dragging top to bottom and vice-versa.
When everything is on the same plane, if the taskbar is still double-high (or an inch high), it can be grabbed and dragged down to normal.... so we hope.