if your user doesn't have a password you can connect both hard disks to the new ps, boot the livecd and from it, copy, move or delete the files you need
i usually have two hard disks, one with the stuff i use the most and other with files i need to store
i recently got a external hard disk i use for work and for my personal use so i don't have a single place(don't put all your eggs on one basket)
if the hard disks are old too, maxtor by any chance, more than 8 years, time to replace them too, i don't trust on a hard disk much after 5 years
yes, it is clear what you can save and what not, i used to change the main 3 components alot, mainboard, cpu and ram and keep the rest including hard disks, psu, dvd drive, atx case, mouse, keyboard, monitor and speakers, are you on this same position or most of your hardware deserves a replacement?