Hi William,
The recovery partition can be created using Diskpart commands.
1] Please open Disk Management and maximize it. Adjust the column widths in the top pane to make all the entries visible. Post a screenshot.
2] Launch msinfo32.exe, and click System Summary. Resize the columns in the right pane to make the entries visible, and post a screenshot.
3] Open the admin Command Prompt and run:
bcdedit
reagentc /info
Post the output.