Here's a simple test that I've never known to fail in this classic English problem:
Phrase the statement as two separate statements, one referring to Jon and the other to you. In the one referring to you, if 'me' sounds correct, use 'Jon and me', if 'I' works, use 'Jon and I'.
A couple of examples to illustrate:
He gave the money to Jon and (I/me).
Try it using only you:
He gave the money to me.
As you can see, 'me' is the winner because using 'I' here would be horrid.
Jon and (I/me) are going to see a play.
Unless you are a caveman, you wouldn't say 'Me am going to see a play', so 'I' is correct here.