Don't bother with the screen shots.
Maybe I should first mention: Do you have your data backed up? If so you can reinstall and recover... Or use a LiveCD and backup your data to a USB drive or rsync over the network.
But if this is right you will need to fix the filesystem before recovering the data...
First hit of google Maverick init not found, pass value to init http://ubuntuforums.org/showthread.php?t=1594621
All they did was manually fsck the filesystem. fsck is file system check for ext2,3,4 file systems. They didn't seem to cover how they did it all that well since it seems to have just one partiton, so here is a little trick that might make it easier. Put a file called forcefsck in the root of the partition or partitions will force the file system check.
Boot with a LiveCD, probably what you used to install Ubuntu. Use whatever GUI file manager thing they have, the web page talks about using gparted, I thought that was for partitioning, not mounting drives... In kde dolphin is the default GUI file manager, to mount the partition or partitions, click on the left side. Make sure it is a ext partition, you don't want to do this on xfs or other partition types without making sure you don't need other options or whatever, ie xfs has its own repair utility.
Open a terminal...
df -h, or lshw or dmesg to determine the filesystem you want.
mount with no options to check the filesystem type
sudo touch /forcefsck using the correct path.
For example I plugged in a 40GB PATA drive with one of those USB adapters.
Mounted it with dolphin.
cp <at> meerkat:~$ df -h
Filesystem Size Used Avail Use% Mounted on
/dev/sda1 19G 4.3G 15G 23% /
/dev/sda7 270G 22G 248G 8% /home
/dev/sda6 9.2G 2.3G 6.5G 26% /mythbuntu
/dev/sdb1 36G 22G 13G 64% /media/disk
cp <at> meerkat:~$ mount
/dev/sda1 on / type ext4 (rw,errors=remount-ro,commit=0)
/dev/sda7 on /home type xfs (rw)
/dev/sda6 on /mythbuntu type ext4 (rw,commit=0)
/dev/sdb1 on /media/disk type ext4 (rw,nosuid,nodev,uhelper=hal)
cp <at> meerkat:~$ sudo touch /media/disk/forcefsck
cp <at> meerkat:~$ sudo umount /media/disk
and reboot without the CD...
Hopefully all goes well, it will take longer than normal to boot since the fsck can take a while depending on the size of the partition(s).
If it doesn't work you will likely see some message about having to run fsck manually. Repeat the above steps and run fsck on the partition. In the example above I would run fsck /dev/sdb1.
My first thought was it sounds like grub, the boot loader, can't find the root filesystem. For that see:https://help.ubuntu.com/community/Grub2