Simple hashing code with excessive conditional statements
You should really take a look at argparse: the argparse module makes it easy to write user-friendly command-line interfaces. It will even take care of writing the help for you.

Even if you will apply very little of the following (since you should really use the argparse module), I'll give you some advice anyway.

str.lower()

This:

if hashmethod == "MD5":
    hashCalculator(filename, "md5")
elif hashmethod == "SHA1":
    hashCalculator(filename, "sha1")
elif hashmethod == "SHA224":
    hashCalculator(filename, "sha224")
elif hashmethod == "SHA256":
    hashCalculator(filename, "sha256")
elif hashmethod == "SHA384":
    hashCalculator(filename, "sha384")
elif hashmethod == "SHA512":
    hashCalculator(filename, "sha512")


could just be:

hashCalculator(filename, hashmethod.lower())


Coding style

Follow the official coding style, the main rules are summarized here.

getattr()

This:

if hashmethod == "md5":
    m = hashlib.md5()
elif hashmethod == "sha1":
    m = hashlib.sha1()
elif hashmethod == "sha224":
    m = hashlib.sha224()
elif hashmethod == "sha256":
    m = hashlib.sha256()
elif hashmethod == "sha384":
    m = hashlib.sha384()
elif hashmethod == "sha512":
    m = hashlib.sha512()


could just be:

m = getattr(hashlib, hashmethod)


Multiple line strings

Don't do this:

print "\n"
print "----------------------------------------"
print "\tWelcome to Hash Calculator"
print "----------------------------------------"
print "\n"
print "--help"
print "\n"
print "In order to calculate the hash value of a file, your command line syntax"
print "must be written as below:-"
print "\n"
print "\thashcalculator -f [file] -h [hash method]"
print "\teg. hashcalculator -f notepad.exe -h SHA1"
print "\n"
print "The recognised hashing methods are MD5, SHA1, SHA224, SHA256, SHA384 and SHA512"


Do this instead:

msg = """
----------------------------------------
\tWelcome to Hash Calculator
----------------------------------------

--help

In order to calculate the hash value of a file, your command line syntax
must be written as below:-
\thashcalculator -f [file] -h [hash method]
\teg. hashcalculator -f notepad.exe -h SHA1

The recognised hashing methods are MD5, SHA1, SHA224, SHA256, SHA384 and SHA512"""

print msg