First, activating "legacy support" was the wrong thing to do. On a computer with Windows 8 pre-installed, activating legacy support in the firmware makes it possible to go down paths that will create new problems, and in fact that's precisely what you've done. (That said, sometimes it really is necessary to activate this support, but it's more likely to cause problems than to solve them.)
Second, the "boot files... are far from the start of the disk" message is almost certainly a red herring. This can be a factor with certain disk sizes and certain BIOSes, but you've got an EFI implementation, not a BIOS. An EFI should be able to boot from kernels located anywhere on any disk currently available. Certainly your 1TB disk should pose no problems. Thus, everything you did from that point on was unnecessary at best and problem-producing at worst.
Despite your activation of legacy support in the firmware, it's conceivable that your system would have booted Windows after you ran Boot Repair. You don't say whether you tried to do so at that point, though, so it's unclear if it would have worked or if you just tried to fix the "far from the start of the disk" non-problem without testing it.
Somewhere along the line you seem to have installed the BIOS (legacy) version of GRUB, which may be what you're booting by default (to get the grub rescue> prompt). It's conceivable that disabling legacy support in your firmware will cause the system to boot straight to Windows or straight to GRUB's EFI-mode installation. If it boots to Windows, you should still be able to get to GRUB by hitting F12. If it boots to GRUB, then you should be able to boot Linux, and possibly Windows. (I recommend trying the first two Windows options. The final three Windows options are unlikely to do anything useful.)
If you try this and get GRUB working as the default, you can try using GRUB Customizer to clean up the GRUB menu a bit. I'm not very familiar with this software, though, so I can't be more specific about how to use it.
Another thing you could try is to install my rEFInd boot manager. If you install the Debian package and if everything works perfectly, this will give you a menu with options for Windows, for Ubuntu via GRUB, and for Ubuntu directly. You can then remove extra boot entries by deleting unnecessary .efi files in the /boot/efi/EFI directory tree or by editing /boot/efi/EFI/refind/refind.conf and uncommenting and adjusting the dont_scan_files or dont_scan_dirs options.
You may also want to review your partitions. Your Boot Repair output indicates that you've got four NTFS partitions, and I suspect at least one of those is unwanted/unnecessary, but I can't really be sure of that. You also shouldn't need /dev/sda6 or /dev/sda11 once you've fixed everything.
Solved:
Thank you all for your suggestions, after reading some more similar reports, it turns out it was simpler than I thought. After selecting the Try or Install, the screen brightness was set to 0. So I could see only pure black. Using the laptop brightness keys worked and the live Ubuntu is working fully ok. A bit stupid, but the screen was so black, I did not to came to the idea of using the brightness buttons (one has to press it two-three times before one can see the light on the screen).
To answer some of the questions:
For the usb, I tried Unetbootin, usb-creator-gtk (crashed), Live USB Creator, and mkusb script from http://ubuntuforums.org/showthread.php?t=2172971 on Ubuntu. The current usb I used for the last test is the one created with mkusb script. May be the others have worked too, but I could not tell.
I disabled secure boot in bios, and I changed the boot menu order in bios. In U330p bios can be reached via the small nova button - I am using a small screwdriver to press it.
After Try Ubuntu without installing from the grub, one has to use laptop brightness key to see the screen.
So I will install Ubuntu next :), thanks for all the help.
Best Answer
The first thing you should try is disabling Secure Boot -- but do not place the system in CSM/BIOS/legacy mode. The comments about Secure Boot that you reference are overly optimistic. In particular, although it does seem to work as planned for some systems, on others it most emphatically does not work as intended. If yours isn't working as intended, the symptoms would likely be precisely the ones you see. Thus, you should first try disabling Secure Boot. If it boots at that point, you can either leave Secure Boot disabled or try to fix it yourself. See my Web page on Secure Boot for more on this topic.
If disabling Secure Boot doesn't help, then I recommend you leave it disabled and try my rEFInd boot manager. You can try it without changing your disk configuration by using the USB flash drive or CD-R image; or you can install it from Windows. (If you do the latter, be sure that you install the driver for whatever filesystem you use on your Linux root (
/) or/bootpartition, though.) In a typical configuration that does not have a separate/bootpartition, a rEFInd CD-R or USB flash drive should be able to boot either Linux or Windows directly and without further configuration. If you try rEFInd from an external disk and want to use it permanently, you can install it from either Windows or Linux.