What you're describing is a multistep process.
1) First is chord recognition. This is hard to do, but artificial intelligence is making it easier. That said, the only software I'm aware of for a non-programmer to use that also works pretty well is Chordata: here's the download link, but be careful, like all download sites it tries to get you to download crap along with it. Click the button that says 'trusted download', and then on the next page Answer 'no' to the popup that asks you whether you want to download a 'helpful download manager'. When you run the installer, I can't remember if it tries to get you to install other stuff too, just pay attention and opt out. Unfortunately, that's the state of software today.
Chordata won't save the chords for you, unfortunately, you'll have to write them down. This is a feature, not a bug, because like all automatic processes there will be a few errors you'll want to weed out by ear.
2) As for then playing those chords, there are a few VST that can do that. Chordz is free, but you'll have to record the basics of the midi track. Key chords is $15, but it allows you to just name the chords and it will play then, plus there's even an iPad app.
I'm sure other solutions exist for the separate parts, but I've not yet heard of anything that automates the whole process.