Ubuntu – Installing Ubuntu problem “the partition assigned to starts at an offset”

The overlapping data suggests that you did not have a GPT disk to begin with, but in fact had an MBR disk and were booting in BIOS mode. (One of gdisk's features is that it automatically converts from MBR to GPT when you launch it on an MBR disk.) If I'm right, you can probably restore the MBR as follows:

1. Launch gdisk, as in your example.
2. Load the (converted-to) GPT backup data, as in your example.
3. Type r to enter the recovery & transformation menu.
4. Type g to convert the GPT data to MBR form (in memory). You'll see a new MBR command prompt.
5. Type p to view your converted-to-MBR partition table.
6. Review the output to be sure that all the partitions are present -- none should be listed as omitted in the Status column. You may want to review the FixParts documentation, as FixParts uses this same menu, and the documentation describes the options in more detail.
7. Once you're satisfied that all your partitions are present and set as they should be, type w to save your changes and exit.

OTOH, if you're positive that the disk was in GPT form and that the computer was booting Windows in EFI mode, then your partition table was simply damaged to begin with. In this case, you may need to delete that final partition and re-create it a little bit smaller to make it fit; gdisk won't let you save a damaged partition table.