I am trying to backup my computer files, so that i can migrate my data
to another laptop. I am just not able to copy my .pst files ( i have
two files that i want to copy a) Outlook.pst its a 4.7 GB file and
Archive.pst , its a 1.7 GB file. I have tried to use the pst backup
tool from microsoft , i have tried to copy or move, i have tried to
export from my current .pst file to a backup.pst but nothing works.
While copying it gives a " Cannot copy, Cyclic redundancy Check" and
the copying shuts down. What can i do ?

Make sure that files are not corrupted

you may use this program
http://www.softwarepatch.com/security/crsecuritydownload.html

That seems like quite a tricky error.  A cyclic redundancy check (CRC)
is a transmission error checking method.  When data is sent from one
place to another on a computer (or multiple computers) the sender
computes a number that is derived from the data being sent.  The
sender and receiver both use the same formula to derive this number. 
So if the data doesn't change during transmission both the sender and
receiver will compute the same number.  The CRC is a check that the
number stays the same at the transmitting and receiving ends.  If this
is not the case then the 'Cyclic redundancy check' error will pop up
indicating that there was an error during transmission.
So your CRC error means that the data is somehow being changed between
when it is sent and received.
There are a number of ways that this can happen, especially with very
large files such as the ones you are using.  Often the problem is a
result of errors in the hardware (e.g. corrupted files on a hard
drive).  You probably should do a error check on your hard drive - in
windows XP double click on my computer -> right click on the hard
drive -> tools -> error checking.
Now if we verify that the hard drive is ok the problem is likely that
the data somehow gets altered during transmission.  It's possible that
outlook writes to this file while you're copying it over.  What you
probably want to do is ensure that outlook is not running in any form
when you do this.  I would start the computer in Safe Mode (hit F8
before windows starts and select safe mode) then copy the files from
there (choose the with networking option if you want to copy over a
network).
If this still doesn't help then you should make sure that there are no
errors in the transmission of the files (e.g. network problems).  Try
a different method of copying the files such as using a dvd-r or over
a network.  Verify that you can copy different files using this
method.  Hope these suggestions help.