Balanced smileys check algorithm (part 2)
Some notes:


Variable naming 


Can be greatly improved by the use of an IDE like IDEA which supports trivial variable renaming.
Don't use single character variables, index and character (or even char) is much more readable than i and c.
It's not immediately obvious what any of the variables are. 

You only have one test case. There should be test cases including and excluding each of the types of content of a message. If you get started with the simplest one you can even use TDD to get to a working but simple design.
Knowing the index of the unbalanced parenthesis would be nice.
Checking the number of parentheses is not enough, you have to whether they match up. For example, your algorithm fails (reports True when it shouldn't) on strings like )(.
The assignment calls for a recursive solution:


  A message has balanced parentheses if it consists of one of the following: […] An open parenthesis '(', followed by a message with balanced parentheses, followed by a close parenthesis ')'.


This means that within each pair of parentheses there must be a valid message, meaning all the rules apply within them.