locally stored passwords are encrypted so simply getting to them on the hard drive is not good enough. i'm pretty sure you have to fire up that installation again to get them accessible. you can try booting the drive with your new system though it is unlikely to work.
you don't need it to work forever, just a few minutes so you can export the data, so its worth a shot as an easy first step. after that you're in for a lot of work that may or may not help. i use firefox sync myself to keep it all in the cloud so i can use everything on multiple machines as needed.
see if it will boot for you on the new machine, then go from there.