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#variable defination#
lower="abcdefghijklmnopqrstuvwxyz"
upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ"
valid=True
x=0
g=0


string=input("enter a string:")

#data validation#
for char in string:
 if char in "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ":
 valid=True
 else:
 valid=False

#finding the character#
if valid:
 for char in string:
 g+=1
 for ele in upper:
 if char!=ele:
 x+=1


print(lower[x]+string[g::])

**I can't get it to work, it keeps iterating through the entire string without the condition ever being met. **

I tried to minimize changes from your original code (But remember, it's obvious that other solutions are much better.)

#variable defination#
lower="abcdefghijklmnopqrstuvwxyz"
upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ"

string=input("enter a string:")

#data validation#
valid = True
for char in string:
 if char not in lower + upper:
 valid=False

#finding the character#
if valid:
 result = ""
 for char in string:
 if char in lower:
 result += char
 else:
 # uppercase character
 for i in range(len(upper)):
 if char == upper[i]:
 result += lower[i]
 break

 print(result)

Since you are allowed to use lowercase and uppercase character inputs, you can create a dictionary mapping between them and use str.join with a list comprehension:

from string import ascii_lowercase, ascii_uppercase

d = dict(zip(ascii_uppercase, ascii_lowercase))

string = input("enter a string:")

res = ''.join([d.get(i, i) for i in string])

It's not clear whether this satisfies your "no in-built function" requirement.

You can create mapping(dictionary) between uppercase and lowercase alphabets such that upper_to_lower[uppercase] should give you lowercase. You may refer below implementation as reference though.

import string

def to_lower_case(word):
 # construct auxilliary dictionary to avoid ord and chr built-in methods
 upper_to_lower = 
 for index in range(len(string.ascii_uppercase)): # this is 26 we can use it as constant though
 upper_to_lower[string.ascii_uppercase[index]] = string.ascii_lowercase[index]

 result = ''
 for alphabet in word:
 if alphabet in string.ascii_uppercase:
 result += upper_to_lower[alphabet]
 else:
 result += alphabet

 return result

# sample input
In [5]: to_lower_case('ANJSNJN48982984aadkaka') 
Out[5]: 'anjsnjn48982984aadkaka'

You can also write an index method to get the index of an uppercase character in the upper string:

lower = "abcdefghijklmnopqrstuvwxyz"
upper = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

def index(char):
 i = 0
 for c in upper:
 if char == c: return i
 i += 1

Then you can convert your string to lowercase like this:

#data validation#
# ...

#finding the character#
s = ''
if valid:
 for char in string:
 if char in lower: s += char
 else: s += lower[index(char)]

print(s)