So many hard drives!
/dev/sda contains data you access from Windows (I believe from the label:
"Data"). I believe from the "boot" flag that the bootloader (GRUB) was
installed on this drive. If /dev/sda2 really contains data (look at its
files, double-clicking on "Data", on the desktop), then it is not right. If
I understood well, you cannot boot Windows anymore. I would try to remove
the "boot" flag from /dev/sda2. You can do that from GParted, right-clicking
on the row for /dev/sda2, then on "Manage Flags" and finally unchecking
"boot".
/dev/sdb contains a small (100 MiB) system partition for Windows (I believe
from the label "System Reserved"), whatever this is (again, I have not
administrated any Windows system after Windows XP), and a rather large
(119.14 GiB) Windows partition. It may be the actual Windows system because
the "boot" flag is set on this drive too. You can check by looking at its
files, double-clicking on "128 GB Volume" on the desktop.
/dev/sdc contains a small recovery partition (I believe from the flag
"msftres") and a very large (3.64 TiB) partition where are most of your user
files you access from Windows, I believe (you can take a look at these files
by double-clicking on Jun2014, on the desktop). /dev/sdc2 has quite a lot of
unused space: 1.24 TiB. You could take some to install Trisquel. GRUB could
then be in /dev/sdc's Master Boot Record (MBR)... but I do not know if GRUB
would to be able to boot Windows, on another drive (I have never worked with
systems installed on different drives).
/dev/sdd contains a small partition with Windows' backup system (I believe
from the label: "Backup Sys Rsrvd"), whatever this is, and a quite large
(232.69 GiB) partition, which is a backup of the Windows' C: drive (I believe
from the label: "Archive C Drv"). It is full what probably explain that the
problem you face when you try to backup Windows (but you could copy the files
somewhere else, not using Windows' backup system or configuring it to use
another drive if it is large enough). You can look at the backup by
double-clicking on "Archive C Drv" on the desktop. The filed in the backup
may not be directly readable in this way though (the backup may be
compressed, incremental, etc.).
As you wrote, /dev/sdi is your USB key. I am quite surprise of the name
/dev/sdi. I believed the letters of the drives were following the alphabet:
don't you have a /dev/sde, /dev/sdf, /dev/sdg and /dev/sdh? Not that four
hard drives is too few!
No trace of GNU/Linux. Did Trisquel's install go all the way? It normally
takes (tens of) minutes.
