If you've already recovered your data, there is no necessity to run another diagnose again.
Sector size message can appear if you use a disk on another PC, because disk controller is different.
Did you create your Recover-DVD's?
Laptops are a kind of tricky.
Manufacturer often use a different partition type instead of FAT or NTFS to hide partitions.
It's intended that user can't change anything.
Often the first partition contains some utilities that you can start diagnostic etc..
The last partition ist mostly recovery.
Also the partition table is sometimes modified, so that you can press a certain key during startup to get to diagnostic and recovery.
TestDisk works Intel or GPT-standard and if you write a partition, you can override modification in your partition table.
But it's only valid for modified partition tables.
I've checked the whole topic to find more information.
On another PC, it would be possible that you have no ownership or administrator privileges on partitions?
But it's not advisable to change ownership nor privileges.
It can cause a lot of confusion.
To figure out what kind of partition types HP uses, you should call or write HP support.
The only affect would be that partitions under windows are visible.
You can have more drivelettes and drive letters can be changed.
But it could be done later.
Todays most used partition type to hide partitions is Windows REstore for recovery.
Boot partitions are often System Reserved and have no drive letter.
Efi partitions are often not visible either.
Also, I've seen that your first partition does not contain any boot files.
But the third partition contains some.
Have a look at your third partition:
http://forum.cgsecurity.org/phpBB3/down ... hp?id=3392
You can consider to make it bootable and test it.
Compare with your first partition it only contains a folder called recovery:
http://forum.cgsecurity.org/phpBB3/down ... hp?id=3392
There are no boot files but it was set to star for active and bootable.
It would be worth a try to change it and write your partitions using testdisk again.
You should run Analyse and Quick Search.
Set your third partition as described above to Star * for active.
Set the other two partitions to P for primary only.
Use TestDisk to write your partitions.
Put your disk back into your laptop and try to boot.
Please let me know.
There is still something what I don't know at the moment and would be important to clear:
Your boot partition contains some efi information.
But on your first photos before you used TestDisk to write your partitions, your partitions were displayed as Intel and not as EFI GPT (UEFI).
From your log file:
Partition table type default to Intel
Disk /dev/sdb - 1000 GB / 931 GiB
Partition table type: Intel
UEFI can work with Intel-MBR too.
If you experience any problems, please let me know.
A pretty good question would be, did you have an Intel or GPT-disk before?
It would be possible to convert your disk to GPT but it's not as easy.
It means:
You have to delete all partitions using your disk management console.
You have to rightclick into the small square at the left side at your disk in the disk management console and convert it to GPT.
Afterwards you have to run TestDisk Analyse and Quick Search again.
Setting your bootable partition to Star and the other ones to P for primary only and write the partition structure using Write into your GPT partition table.
But only in case you'll need it.
Fiona