Hi Syndi, perfect conditional used in your sentence can only be used with the participle of the verb.
would+have + participle
This is incorrect, as the correct sentence is the one you mentioned.I would have come to New York" which, in truth is bad English
If you had let me, I would have come to New York."If you would have let me, I would have came to New York"
I should be very surprised to hear that.I would have went there ??? if I could have..." instead of "I would have gone".