From the screen photo, It seems like the installer wiped your hard drive. This was a known issue before 14.04, but it should have been fixed since, according to the bug status. If it really is as you said, please file a new bug report for the Ubiquity package.
I hope you made a backup before attempting a reinstall. If not, let this be you a lecture.
If you are using a SSD, you can basically give up all hopes. SSDs use a feature called TRIM, which erases deleted and invalid data blocks as to keep the drive fast.
If you need to recover files, stop using the installed system immediately and find another harddrive which you can use to back up your data, preferrably empty and big enough to hold your files - at least those which you manage to recover. Please always keep in mind that file recovery is basically gambling, no matter which tools you use.
Now boot the Live Ubuntu on the installation medium ("Try without installation") and open a terminal (Ctrl+Alt+T). In there, use the following command to install the recovery suite TestDisk:
sudo apt-get install testdisk
This will not affect your problematic hard drive, as the program will be installed to RAM (or live system persistency, if set up) only.
Now, TestDisk is a pretty straight-forward, interactive recovery suite. To start it, you use the following command:
You may first want to search for lost partitions. It should be TestDisk's first menu option. (Partition table Intel/PC/msdos). If you are lucky, TestDisk will manage to find the deleted partitions and gives you the option to create a new partition table. This will likely make the installed system unbootable.
When the program manages to restore the partition table (even partially), you should be able to mount the formerly lost partitions and you may find your personal files. If so, copy them to an external hard drive (the one I advised you to get before.)
If not, use another tool called PhotoRec. It should already be installed with TestDisk and is also very simple to use. In this case, you may however not be able to restore the files' names.
For further information, read this very good article.
Good luck! (You'll need it, if you don't have a backup)
As for your Windows, the default recovery partition is now gone. If you want to reinstall it, get a installation disk image from Microsoft (I hope they still provide any), put it on an USB or DVD and install it using the product key provided with your computer (may be inside the case). If you can't find any PK sticker, you should contact the PC manufacturer and ask for help. Some don't provide those stickers any more.
Edit: Sometimes, the PK is stored in the BIOS, so a destroyed partition won't erase it. You will know, if your Windows activates itself without you entering a PK.
Btw. you can take screenshots using the PrtSc key in Ubuntu, and they will be saved in