Can you post a screen capture of this? I can't imagine what you're describing.
What are the Clips, that you are attempting to place the Transitions between?
Can you drag a Dip-to-Black (is kind of "special" over most others) to either the "cut" between those Clips, or to one end of the Clip?
Also, if you are in Quick Mode (basically a revised Sceneline Mode, but with more power, added in PrE 11), or Expert Mode. If Quick Mode, switch to Expert Mode and try again.
If you get any error messages, when you do drag the Transition successfully, please copy down the exact text in that message, and post it here.
When I try to use a transition, the transition I choose, regardless of which one I hae chosen, does not move with the cursor. I get a circle with a line through it (which I take to mean no transition). What am I doing incorrectly and how can I remedy the problem?
When you choose a transition, a blue box forms around it as an indication that it is selected. The box does not move.
Put the mouse curser in the middle of the blue box and HOLD IT DOWN. Do not let up. As you drag out of the blue box and Transitions Tab, it does turn into a tiny circle with a line through it that is attached to the mouse pointer arrow. If you let go, you have to start over.
The circle is so tiny I could not get a screen capture to post. But it is a circle with a line through it that in other worlds would suggest a mistake is being made.
Sometime the circle disappears as you drag over various parts of the screen and all you see is the mouse pointer. Don't give up. Keep holding the button down.
Continue to drag it to the exact spot on the timeline where two video clips join. It will be hard to see if you don't have your timeline enlarged or you have a low resolution monitor.
If you still have the mouse button held down, it will change to a "transition" symbol when you get the mouse pointer to EXACTLY the right spot where two clips join on the Video line. This new symbol is not big either. You have to look hard. With the new symbol visible, you can finally release the left mouse button and the transition will be applied.
So many of these things are subtle, not obvious and don't make sense. I struggled with a lot of it until I watched the complete course on lynda.com taught by Steve Grissetti. It cost me $25, but things that are not intuitive quickly work because you can watch him make sense out of it.
If everyone watched Steve's course, the only questions on this forum would be about bad video drivers!