The BIOS menu shows and recognizes my internal hard disk drive but when I try to install Ubuntu from a LiveUsb, the installation wizard where we are supposed to key in the mount point and the partition of install just shows nothing.

The wizard just vanishes.

Yesterday, I was trying to cut some documents from HDD to pen drive. Ubuntu displayed a message that the files could not be moved. Also following this message, the documents were nowhere(neither in the pen drive nor in the original location in HDD partition).

So, I went to the original file location(in HDD partition) and performed an undo move operation.

This resulted in system crash and then my system is unable to boot.

The system says that no operating system is installed and asks me to install either a Live USB or operating system as such.

Also when I was doing this move operation, my system was a bit heated up. Could this be an issue?

When my system startsup, the HDD indicator LED glows just as normal.

Boot into rescue mode and see if you can find the disk. As long as the partition table is in tack you should be able to restore it.
You could try THIS to recover the lost partition table

Check smart status of drive with smartctl. Also you may run 'badblocks' to see bad sectors in drive.

fdisk -l /dev/sda

Output is

Cannot open /dev/sda

---------- Post added 05-08-15 at 08:51 PM ----------

Besides can you help me using badblocks

If it can't open sda then badblocks is no use. You should run SMART tests using smart-mon-tools or use your drive manufacturer test tools.

Re post #4.

The command is : $ sudo fdisk -l /dev/sda