Gavin:
Here's the "rub" with the laptop, logic pro and M-Audio Fast Track suggestion.
Aside what was already mentioned by Kanthos and John (which were both spot on), all of the aforementioned acts who are using PC's and sequencing programs, as well as VSTi's to "augment" sounds are using redundant systems, running concurrently. All the bigs have two (and some like Interpol, Massive Attack, Radiohead have THREE systems running, fully synced at one time). Why? Computers crash. It's not a question of IF, it's just a matter of when. A fully digital rig is great, if you have a redundant system to back you up. If not, you'll be standing on stage, accompanying yourself when your PC goes down.
If you're looking for single key trigger for certain parts (hits) and recorded voices, you need sampling capability (both play and record).
If you want to play chords, via one key or button, that's more in the "arranger" keyboard area, but you'll forgo things like sampling.
One machine that would likely fill all your requirements would be the Korg M3. It has assignable buttons or pads, that you can assign and trigger "chords" with, sampling, sequencing and fully DAW/sequencing integration. The Korg M50 has similar features, except no sampling.
The Yamaha Motif's can do all the above, except they don't have those trigger pads or buttons to assign chords to, however you can do it by assigning chords in patterns, arpeggiators, performances or sequences.
I'm sure there are other keyboards that have similar capabilities, but since I play everything live, and sing at the same time, I've never explored these other alternatives for live performance.
Anyway you slice it, you're looking to replace technical ability with technology and in a live situation, that often comes out "mechanical." If you've got a group of "hot musicians", they're not going to be too fond of playing "back up" to a machine driven frontman.
At the very minimum, you're asking for a pretty tall order and assuming you find that magical technological solution, then you have the learning curve, setup and assimilation to make it all work.
Learning the parts and additional practice sounds easier (and less expensive) to me!!
Your mileage may vary.
Good luck.
Ray