There are many mysterious bug-looking aspects in your code. The wrong order of definition (assuming you do need the search function to be a nested one) and the syntax error from the empty while loop have already been observed, but there are more...:
def dfs(problem):
stack.push(bache)
search(root)
what's bache, what's stack, what's root? If they're all global variables, then you're overusing globals -- and apparently nowhere ever using the argument problem (?!).
while stack.isEmpty() != 0:
what's this weird-looking method isEmpty? IOW, what type is stack (clearly not a Python list, and that's weird enough, since they do make excellent LIFO stacks;-)...? And what's ever going to make it empty...?
def search(vertex):
closed.add(vertex)
...don't tell me: closed is yet another global? Presumably a set? (I remember from a few of your Qs back that you absolutely wanted to have a closed dict, not set, even though I suggested that as a possibility...
for index in sars:
...and what's sars?!
stack.push(index)
return stack
what a weird "loop" -- one that executes exactly once, altering a global variable, and then immediately returns that global variable (?) without doing any of the other steps through the loop. Even if this is exactly what you mean (push the first item of sars, period) I don't recommend hiding it in a pseudo-loop -- it seriously looks like a mystery bug just waiting to happen;-).