Wait for somebody else's opinion, but here's mine.
Notice this from your log:
Drive: sda _____________________________________________________________________
Disk /dev/sda: 512.1 GB, 512110190592 bytes
255 heads, 63 sectors/track, 62260 cylinders, total 1000215216 sectors
Units = sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
Partition Boot Start Sector End Sector # of Sectors Id System
/dev/sda1 206,848 292,184,795 291,977,948 7 NTFS / exFAT / HPFS
/dev/sda2 * 292,186,112 293,181,439 995,328 27 Hidden NTFS (Recovery Environment)
/dev/sda3 293,183,486 1,000,214,527 707,031,042 5 Extended
/dev/sda5 970,917,888 1,000,214,527 29,296,640 82 Linux swap / Solaris
Warning: extended partition does not start at a cylinder boundary.
DOS and Linux will interpret the contents differently.
Yes, your main ext4 partition is in fact absent, however your swap partition is still there. That could possibly be an indicator that the destruction isn't too serious.
The way I see it you have two options:
- Attempt recovery
- Reinstall Ubuntu
For attempting recovery, the first thing you're going to need to do is create a live USB drive. As you seem to be a technically inclined person, I'll simply recommend using the program from http://pendrivelinux.com
I found this success story about ext4 recovery even though the poster had LVM: http://ubuntuforums.org/showthread.php?t=1376383
He used the program testdisk, so I would suggest that as well.
Do you have an external HDD >= in capacity to your internal HDD?
If not, you need to decide how important this recovery is to you. Remember, your data is probably still there somewhere.
But in order to recover it, you will be performing dangerous operations with the potential to destroy the vulnerable data.
So assuming you have the right sized external HDD as I mentioned previously, boot from that live USB you created earlier and
dd your internal drive to the external one, like so:
#Keep in mind this will destroy everything on the external HDD. You'll need to replace the path to the external HDD's partition accordingly, or else you will most certainly facilitate further destruction.
sudo dd if="/dev/sda" of="/dev/sdb"
That will take several hours to complete. So give it some time.
Afterwards, disconnect your external drive.
Congratulations! You now have a complete drive image, meaning that if you completely wreck the entire partition table on your internal one, you can still restore to the exact state you are in now
Now that you have said drive image, have a go with testdisk and see what it comes up with.