I ran the recommended repair for the boot repair, and it seemed hopeful. (Note that I ran it while in "Try Ubuntu" mode, running from the CD.) Here is the message it gave me once it was done:
That didn't help, so I ran Ubuntu off the CD again and ran the BootInfo summary. This is what I got: http://paste.ubuntu.com/7128583/
Boot successfully repaired.
Please write on a paper the following URL:
In case you still experience boot problem, indicate this URL to:
firstname.lastname@example.org or to your favorite support forum.
You can now reboot your computer.
Please do not forget to make your BIOS boot on sda1/EFI/ubuntu/shimx64.efi file!
You may want to retry after deactivating the [Backup and rename Windows EFI files] option.
The boot of your PC is in Legacy mode. You may want to retry after changing it to EFI mode.
Any idea what I should do next?