Pythonic code to convert 3 digit number into all possible letter combinations
First, Python 2 is going to be no longer supported in less than a year. If you are starting to learn Python now, learn Python 3. In your code the only differences are that print is a function now and no longer an expression (so you need ()) and that raw_input was renamed input (and the Python 2 input basically no longer exists).

Your building of the root dictionary can be simplified a bit using a dictionary comprehension:

from string import ascii_lowercase

num_to_letter = {str(i): c for i, c in enumerate(ascii_lowercase, 1)}


For the first three different permutations you can use tuple unpacking:

first, second, third = sequence_to_convert


Note that you are currently not validating if the user entered a valid string. The minimum you probably want is this:

from string import digits
digits = set(digits)

sequence_to_convert = input('Enter three digit number \n')
if len(sequence_to_convert) != 3:
    raise ValueError("Entered sequence not the right length (3)")
if not all(x in digits for x in sequence_to_convert):
    raise ValueError("Invalid characters in input (only digits allowed)")


(A previous version of this answer used str.isdigit, but that unfortunately returns true for digitlike strings such as "¹"...)

Your testing and printing can also be made a bit easier by putting the possible permutations into a list and iterating over it:

permutations = [(first, second, third), (first, fifth), (fourth, third)]
for permutation in permutations:
    if all(x in num_to_letter for x in permutation):
        print("".join(map(num_to_letter.get, permutation)))


However, in the end you would probably want to make this more extendable (especially to strings longer than three). For that you would need a way to get all possible one or two letter combinations, and that is hard. It is probably doable with an algorithm similar to this one, but it might be worth it to ask a question on Stack Overflow about this.