Ubuntu 14.04 boot corrupted

Does this help? http://linuxpoison.blogspot.co.uk/2011/06/how-to-reinstall-grub-2-in-ubuntu-using.html

@arochester. I don't have a cd with me. Can you please tell me how to solve the problem manually from command line,?

I went to grub menu and tried to free space but the command bar returned this:

Fsck from util-linux 2.20.1
Fsck from util-linux 2.20.1
Fsck.fat 3.0.26 (2014-03-07)
/dev/sda4: clean, 200719/30072832 files, 3118036/120286464 blocks
/dev/sda1: 32 files, 4407/126976 clusters
Mount: wrong fs type, bad option, bad superblock on /dev/sda1,
                Missing codeoage or helper program, or other error
                In some cases useful info is found in syslog - try
                Dmesg. : tail or so

Mountall: mount/boot/efi [771] terminated with status 32
Mountall: filesystem could not be mounted: /boot/efi

F2 or system setup details.

Boot

Boot list option : legacy/uefi. Uefi selected.
Boot 1: ubuntu
Boot2: onboard nic ipv4
Boot3: onboard nic ipv6
Boot 4: peboot

Gnu grub version 2.02 beta2-9

Screen contains only two options

Advanced options for ubuntu
System setup

Reinstall ubuntu option is gone and does not apoear anymore

Clucking on advanced options for ubuntu opens up two options

Ubuntu, with linux 3.13.0-38-generic
Ubuntu, with linux 3.13.0-38-generic (safe mode)

Clucking on the first link leads to page saying

Loading linux 3.13.0-38-generic....
Loading initial ramdisk....

And that's it. It does not move a bit from there. It does not work at all. It stays just like that.
I can't even go back to previous menu from there and have to switch off switch on machine from there.

Clicking on safe mode leads to page saying
Resume. Resume normal boot
Clean try to make free space
Dpkg. Repair broken packages

Failsafex. Run in failsafe graphic mode
Fsck. Check all file system
Grub. Update grub boot loader
Network. Enable networking
Root. Drop to root shell prompt
System summary system summary

Clicking on normal boot takes to a long command line last 4 line says:

Starting clean /tmp directory
An error occurred while mounting /boot/efi.
Keys: press s to skip mounting or m for manual recovery
Stopping clean /tmp directory

I've already said what happens if clicking on the second option called "clean"

Clicking on third option dpkg says same as second option

Fsck from util-linux 2.20.1
Fsck from util-linux 2.20.1
Fsck.fat 3.0.26 (2014-03-07)
/dev/sda4: clean, 200719/30072832 files, 3118036/120286464 blocks
/dev/sda1: 32 files, 4407/126976 clusters
Mount: wrong fs type, bad option, bad superblock on /dev/sda1,
                Missing codeoage or helper program, or other error
                In some cases useful info is found in syslog - try
                Dmesg. : tail or so

Mountall: mount/boot/efi [771] terminated with status 32
Mountall: filesystem could not be mounted: /boot/efi

Clicking on fourth option failsafex says same as second and third.
Fsck from util-linux 2.20.1
Fsck from util-linux 2.20.1
Fsck.fat 3.0.26 (2014-03-07)
/dev/sda4: clean, 200719/30072832 files, 3118036/120286464 blocks
/dev/sda1: 32 files, 4407/126976 clusters
Mount: wrong fs type, bad option, bad superblock on /dev/sda1,
                Missing codeoage or helper program, or other error
                In some cases useful info is found in syslog - try
                Dmesg. : tail or so

Mountall: mount/boot/efi [771] terminated with status 32
Mountall: filesystem could not be mounted: /boot/efi

Clicking on fifth option fsck says
Fsck from util-linux 2.20.1
Fsck from util-linux 2.20.1
Fsck.fat 3.0.26 (2014-03-07)
/dev/sda1: 32 files, 4407/126976 clusters
dev/sda4: clean, 200719/30072832 files (0.1% non-contiguous), 3118036/120286464 blocks

Mount: wrong fs type, bad option, bad superblock on /dev/sda1,
                Missing codeoage or helper program, or other error
                In some cases useful info is found in syslog - try
                Dmesg. : tail or so

Mountall: mount/boot/efi [771] terminated with status 32
Mountall: filesystem could not be mounted: /boot/efi

Clicking on sixth link grub says the same as second, third and fourth
Fsck from util-linux 2.20.1
Fsck from util-linux 2.20.1
Fsck.fat 3.0.26 (2014-03-07)
/dev/sda4: clean, 200719/30072832 files, 3118036/120286464 blocks
/dev/sda1: 32 files, 4407/126976 clusters
Mount: wrong fs type, bad option, bad superblock on /dev/sda1,
                Missing codeoage or helper program, or other error
                In some cases useful info is found in syslog - try
                Dmesg. : tail or so

Mountall: mount/boot/efi [771] terminated with status 32
Mountall: filesystem could not be mounted: /boot/efi

Clicking on seventh option called network says the same as second, third, fourth and sixth ones:
Fsck from util-linux 2.20.1
Fsck from util-linux 2.20.1
Fsck.fat 3.0.26 (2014-03-07)
/dev/sda4: clean, 200719/30072832 files, 3118036/120286464 blocks
/dev/sda1: 32 files, 4407/126976 clusters
Mount: wrong fs type, bad option, bad superblock on /dev/sda1,
                Missing codeoage or helper program, or other error
                In some cases useful info is found in syslog - try
                Dmesg. : tail or so

Mountall: mount/boot/efi [771] terminated with status 32
Mountall: filesystem could not be mounted: /boot/efi

Today I opened the command prompt in grub rescue and typed "grub"
Reply came: the program grub is currently not installed you can install it by typing : apt-get install grub.
Then I did do so and reply was : W: not using locking for read only lock file /var/lib/ dpkg/ lock
E: dpkg was interrupted, you must manually run dpkg --configure -a to correct the problem.
And then I did do so.
Reply was: unable to access dpkg status area : read only file system.

Can anyone spot the problem from this?
And if yes then how to repair the problem?

1. What is the output of the command

fdisk -l

2. The workaround for the "read only file system" problem when booting into "advanced options - root command prompt" is issuing the following command before trying anything else:

mount -o rw,remount /