I've done the same thing and can say that aircrack-ng can NOT crack the password from a failed authentication handshake.
I just set up my wireless router, my computer with Backtrack and got my phone with the wrong password to try connect to my router. Even though airodump-ng says it's successfully captured a handshake, it's not enough to crack it. Aircrack-ng went through the entire password list without success.
I tried the same password list with a working authentication handshake capture and it got the password in a few seconds (the correct password was near the top of the password list).
I opened the failed password handshake in Wireshark and it says it has captured "Message 1 of 4" and "Message 2 of 4" of the 4 way handshake.
From what I gather, you need at least packets 2 and 3, or packets 3 and 4. Just 1 and 2 will not work.