OK. I finally got around my problem by doing a product Reset (Setup/Control Panel/Reset). That didn't 100% solve the problem, but was enough to allow me to complete my project with Titles and Transitions in place. Oddly, though, creating a new Title required these steps:
1. Click on "T" on the Toolbar
- the image appears but in front where other layers, including the "Your Text Here" box, are obscured
2. Cancel
- in spite of the "Cancel", a Title icon appears on A/V Track 4, the first available one not used by my Project
3. Click on "T" on the Toolbar again
- this time, the image appears but the "Your TextHere" box plus the two other outline frames appear in front where they're visible
4. I enter my text and specify Entry and Exit Motions and click on OK
- a second Title icon appears on A/V Track 1 where I'd expect it to be
5. For certain Transitions, e.g. "Push Left", where the next frame is a photo image that doesn't fill the frame (e.g. a portrait mode pic), the phrase "Your Text Here" is visible in the gap. I got around this by editing the Title appearing on A/V Track 4 and clicking on the just visible frame outline under the image. This is enough to get the "Your Text Here" phrase into the text box in the upper part of the control section where I could erase it and then click OK.
Adding a Title to a brand new project doesn't trigger any of these problems, so, clearly, something got mis-set in my Project settings and I don't have enough experience to determine what it is.