Python 2.x - 79 77

I'm not exactly sure what you mean by "without using any string functions throughout the program."

from itertools import*
print[i for i in map(''.join,permutations(s))if i in S]

Python 3

Effective algorithm

from collections import Counter

n1 = len(string1)
n2 = len(string2)
target = Counter(string1)
tlen = len(target)
test = Counter(string2[:n1])
eq = sum(test[c] == target[c] for c in target)

for i in range(n2 - n1):
    if eq == tlen: print(repr(string2[i:i+n1]), 'at offset', i)
    c = string2[i]
    if test[c] == target[c]: eq -= 1
    test[c] -= 1
    c = string2[i+n1]
    test[c] += 1
    if test[c] == target[c]: eq += 1
if eq == tlen: print(repr(string2[-n1:]), 'at offset', n2-n1)

Uses only length function for looping and substring operation for printing.

And output:

'ipsum' at offset 6
'sipum' at offset 81
'pisum' at offset 452
'muips' at offset 568

GoRuby 2.1

32 chars

n.ch.pe.e{|x|s x.j if h.id(x.j)}

assumes string to search for in variable n (needle) and string to search in in variable h (haystack). Ungolfed version:

needle.chars.permutation.each do |x|
  puts x.join if haystack.index(x.join)
end