Help with Code!

[perfringo]

My question is how do I iteratively sum up all my numbers in a list, without the use of the special function sum()

Just iterate over items in list and add to total (sum means adding all items; do you want sum only positive values?):

>>> nums = [11.5, 28.3, 23.5, -4.8, 15.9, -63.1, 79.4, 80.0, 0, 67.4, -11.9, 32.6]         
>>> total = 0                                                                              
>>> for num in nums: 
...    total += num 
...                                                                                        
>>> total                                                                                  
258.8

NB! Never use sum as variable name. You overwrite built-in function and it will come and 'bite you when you least expect'

EDIT: for only positive numbers value checking must be added:

>>> nums = [11.5, 28.3, 23.5, -4.8, 15.9, -63.1, 79.4, 80.0, 0, 67.4, -11.9, 32.6]         
>>> total = 0                                                                              
>>> for num in nums:
...     if 0 <= num:     
...         total += num 
...                                                                                        
>>> total
338.6