Yes, you can just open disk utility from the utilities folder, but in some cases you will be required to not boot from the HDD to repair the HDD, so you will need the discs, but you can do that without that:
To start disk utility without CD/DVD:
- Start holding apple-(cmd)-key and S-key
- a lot of text appears, wait
- type "/sbin/fsck -yf" (or german keyboard "-sbin-fsck ßzf)
- press return
- it will now check everything and say "The filesystem has been modified"
- repeat the above steps, till it says: "The filesystem seems to be OK"
- restart with ctrl-d
This is called booting in single user mode, you can run other test, too with that.
To start disk utility without CD/DVD:
- Start holding apple-(cmd)-key and S-key
- a lot of text appears, wait
- type "/sbin/fsck -yf" (or german keyboard "-sbin-fsck ßzf)
- press return
- it will now check everything and say "The filesystem has been modified"
- repeat the above steps, till it says: "The filesystem seems to be OK"
- restart with ctrl-d
This is called booting in single user mode, you can run other test, too with that.