Overall slowness, as observed when booting, won't have anything to do with disk permissions or disk corruption, it's a failing hard drive. If you open the Console app and take a look at the All Messages section, you'll see errors on /dev/disk1 or a device named similarly to that, indicating bad sectors.
Since you don't have a bootable DVD that is working, you can prove this by booting in single user mode off the hard drive (hold down command-s when powering on), and running fsck -fy - this will fix any file system corruption without needing to be booted off DVD, and you'll see that its still not running properly when you subsequently reboot.
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-Scott
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