Project Euler #1: Sum of Multiples of 3 and 5 below 1000
I expect you made a typo.  You don't want (i%35)==0, you want (i%5)==0.



The PEP-8 style guide for Python requires 1 space before and after operators, and after commas.  Use PyLint or equivalent tool to ensure you follow all of the PEP-8 guidelines.



check_sum is unused, and can be omitted.



The brackets around the if( ... ): condition are unnecessary.  This is Python, not C, C++ or Java:

    if (i % 3) == 0 or (i % 5) == 0: #divisor condition




There is no need to create a list just to add up all the numbers after the fact.  You are only using each value once, so you could simply add the numbers up as you find them:

def prob_1():

    sum_of_multiples = 0

    for i in range(1, 1000):  # Take numbers up to but not including 1000
        if (i % 3) == 0 or (i % 5) == 0: #divisor condition
            sum_of_multiples += i

    return sum_of_multiples




You should add """doc_strings""" to your functions:

def prob_1():
    """
    Compute the sum of all the multiples of 3 or 5 below 1000.

    Returns:
        The sum of the multiples of 3 or 5, below 1000.
    """

    sum_of_multiples = 0

    for i in range(1, 1000):  # Take numbers up to but not including 1000
        if (i % 3) == 0 or (i % 5) == 0: #divisor condition
            sum_of_multiples += i

    return sum_of_multiples




You can use list comprehension a generator expression (thanks @Graipher) and the sum(...) function to compute the result, without ever creating the list in memory:

def prob_1():
    """
    Compute the sum of all the multiples of 3 or 5 below 1000.

    Returns:
        The sum of the multiples of 3 or 5, below 1000.
    """

    return sum(i for i in range(1000) if i % 3 == 0 or i % 5 == 0)




You can also solve this problem by hand with a pen, a sheet of paper, a calculator and about 1 minute of your time.  A program is entirely unnecessary.