Lost Generated Media icon

If you mean the icon on the event(s) on the timeline, try View - Event Buttons.
Ctrl+Shift+C is the shortcut.

Shuki, there's still no picture :(
Try using the IMAGE UPLOAD icon at the top of your post and follow the steps outlined below.

1. Click the icon.
2. Browse to the image and click "Open".
3. Click "upload image".
4. Click the image name in the top right corner.
5. Click and copy the information in the "Embed" box on the left.
6. Click the "x" next to the image name (I'm not sure this step is necessary but I do it anyway).
7. Close the window.
8. Paste the link into your message.
9. Post the image.

When you make a subclip from a text event, it's no longer a text event which is why you don't see the icon.
Out of curiosity, why did you make a subclip from the original text event instead of doing a copy/paste?

I'm glad I was able to help.
Any NLE can be somewhat overwhelming, especially for someone who has no editing experience.
Feel free to ask questions here and we'll do our best to help you along.
There are several excellent tutorials and articles on the Sony site at http://www.sonycreativesoftware.com/training that are worth checking out.

Shuki, this is my way of "paying it forward" for all the excellent help I've received over the years.
I'm glad I was able to help you in your time of need.