Considering Push Button Conversion...help

Does it matter which trans the cables and mechanism were originally attached to?

So... does the car have the original shifter in it now? If yes, then your transmission must already be a pushbutton unit. Even though '65s had column and floor shifters, the transmissions were still pushbutton style units. If you're using an after market shifter, then the trans must be the later style. Your car would have originally had a 904. So if there's a 727 in there now then some parts have already been swapped out and it's hard to say what exactly will work in your car. You mentioned that the park cable is broken, which makes me think you're already using a pushbutton trans.

In general, The pushbutton mechanisms will work with an aluminum-cased transmission from '65 and earlier. 904s would have come in A-bodies and 727s in B- and C-bodies. Here's a picture of where the shifter cable goes into the bottom, front, driver-side corner of the case.
http://www.1962to1965mopar.ornocar.com/images/transzn7.jpg
There's a second cable that controls the parking pawl when you put the shifter into park that goes in from the driver's side on the bottom where the tailshaft housing meets the main body.
http://www.1962to1965mopar.ornocar.com/images/transzn2a.jpg

Some earlier transmissions have what looks like a drum brake on the end of the tailshaft and basically won't work. Some have iron cases and definitely won't work. '66 and up are shifted using a single rod near where the shifter cable goes in on the pushbutton units.