Google CodeJam 2016 - Python Counting Sheep
In general, it is difficult to follow the logic and the code is not readable.

First, here are some general things you can improve:


N.rstrip() does not modify a string in place and returns a new string instead. Since you are not assigning the result to anything, it does nothing
according to PEP8, you should put underscores between the words in variable and function names - number_of_tries vs numberoftries or digitlist vs digit_list, get_number() vs getnumber()
following the previous note - N is not a good variable name
remove unused import
count = count + 1 can be rewritten as count += 1
put the main logic of the program into if __name__ == '__main__':
use print() function instead of a statement for Python 3.x compatibility
use with context manager when opening file(s) - this will ensure it being properly and safely closed 
use os.path.join() to join the path components (okay, you now need to get your import os back :)
define constants in upper case (PEP8 reference)
use list comprehensions
use .format() instead of string concatenation
use built-in sum() function to for counting
loop over the items directly instead of indexes


The code after applying the changes:

import os

NUMBER_OF_TRIES = 1000
BASE_DIRECTORY = '/home/username/GoogleCodeJam/'
INPUT_FILE_NAME = 'A-large-practice.in'
OUTPUT_FILE_NAME = 'largeoutput'


def get_number(number, number_of_tries):
    print("new case number = {number}".format(number=number))

    digit_list = []
    current_number = number
    for j in range(1, number_of_tries):
        number_as_string = str(current_number)

        digits = []
        for item in number_as_string:
            if item not in digits:
                digits.append(item)

        for digit in digits:
            if digit not in digit_list:
                digit_list.append(digit)

        count = sum(1 for k in range(0, 10) if str(k) in digit_list)
        if count == 10:
            print("count = 10")
            return number_as_string
        else:
            current_number = number * (j + 1)
            print("number = {number}".format(number=number))

    return "INSOMNIA"


if __name__ == '__main__':
    input_file_name = os.path.join(BASE_DIRECTORY, INPUT_FILE_NAME)
    output_file_name = os.path.join(BASE_DIRECTORY, OUTPUT_FILE_NAME)

    with open(input_file_name, "r") as input_file, open(output_file_name, "w") as output_file:
        number_of_cases = next(input_file)
        for case_number in range(1, int(number_of_cases) + 1):
            number = int(next(input_file))
            result = get_number(number, NUMBER_OF_TRIES)

            output_file.write('Case #{case_number}: {result}\n'.format(case_number=case_number, result=result))




Alternative Solution:

We can also improve on both the performance and readability if we would use sets - collecting the digits seen so far until the length of the set is 10 (collected all digits) or we reach the maximum number of tries:

def get_number(number, number_of_tries):
    digits = set([])  # keep track of all seen digits 

    current_number = number
    for j in range(1, number_of_tries):
        digits |= set(str(current_number))  # add new digits to the seen set

        if len(digits) == 10:  # exit if collected all the digits
            return current_number 
        else:
            current_number = number * (j + 1)

    return "INSOMNIA"