OK, when you start up the Mac, right after the chime hold down Apple-S. This will put you into Single User Mode (get ready for some UNIX love ). Once at the prompt, type "/sbin/fsck -yf" and hit return. Let it find what it does and repair. Once it finishes, type it again until you see that it says that the hard drive is OK. Then type reboot. If after the reboot you are able to get in, then once you log in head over to Applications-->Utilities-->Disk Utility and select to repair permissions on your hard drive. After it finishes the first time, run it again to make sure it repaired everything. Reboot.
If the above doesn't help, try this: After the startup chime, hold down Apple-Option-P-R. This will "zap the PRAM." It will reset some settings and will cause the Mac to reboot and you'll hear the chime again. Keep holding down those keys for about 4-5 times after the first startup chime from whence you started holding down the keys. After that, repeat the steps above.
I hope this helps for all of you. If not, then you might have to try something like Disk Warrior or just backup what you can and reinstall the OS.
Shutting down OS X in that manner is a definite no-no. That's probably what is causing all of these problems. I don't think bittorrent is to blame, unless you downloaded one of those rootkits masquerading as an application or music file.
Have you tried creating another user and logging in as that account? Hopefully you won't see any problems with the newly created account, meaning you can just move your files in your home folder over to the new account and delete the old one. Just make sure that you give the new account admin priveleges.
Other than that, you might have to do an archive and install of the OS.
Although it's probably not this, make sure that it's not a hardware problem. If it's one of the iMac G5s that were released this summer you might be OK in this respect. However, if it's one of the first generation iMac G5s then you might have a hardware problem which you should have Apple look at. There have been others with similar problems on the first-gen iMac G5 and they've had to send it to Apple for repair.
Adding the "f" at the end will force a cleaning of the system. Try it again in Single User Mode and do the command I suggested. If the filesystem is journaled, it will tell you to do this even if you do it without the "f" at the end.
dear nixgeek, I tried to tipe in "/sbin/fsck-yf" but nothing happend, it said that there no such a file, when I tiped in fsck ,it told me that the volume is journaled and I have to use-f option to force check. So do you think if I use force check maybe it could help, And how the hell I tell the system to run -f option.
Thanx in advence
Be honest, I dont think they gave me the message that tells anything wrong, neither in FSCK or Disk Utility, FSCK told me the system was modified and Disk Utility said the system need to be repair(although I did a few times).