A couple of solutions here. If you can get the pc to turn on then you can copy straight to the external caddy if you have a spare drive in it Also you could share your C drive and copy everything over the network if available, directly onto your new pc. If not then you can take the hard drives out and put them in the caddy and do it that way as you say.
The issue with the IE 8 favourites can be accessed by logging in as administrator on the old pc if you can get it on. Just change your name at the login prompt to Administrator and leave the password blank. Then go into the C drive select users and pick your user name, documents and settings then select favourites.
That should do the trick