The spinning wheel of death

Please help! I am new to this forum and would appreciate any help anyone could give to help me save my dying mac!
I am running a G4 imac 800Mhz mac os 10.3.9 and the other day after shutting down successfully the previous day,the computer started up and then stuck on the grey screen with the spinning wheel. It eventually gets to the desktop after two and a half hours but I can only open a few programs and not all desktop icons will launch. My main priority is to backup my iphoto and itunes libraries but my normal techniques are not working. I have dragged my iphoto library into toast to burn onto dvd via an external lacie dvd writer but got the 'no permissions - error 5000' box popping up. I then proceeded to attempt to drag the folders onto my external lacie hard drive but now it will not mount at all! Even when I do get my photos on screen it takes about 20 mins instead of the usual 3 mins. Also everything that I plug into the mac will not mount on the desktop. I have tried repairing permissions via disk utility but this didnt do much. I also dont have the original panther disks to reboot. Although I have been using macs for a number of years, I have read many threads regarding the same topic but just get baffled with all the jargon.
I am hoping to upgrade to a G5 (non intel) imac anyway and can startup in target mode by pressing 't' on startup. Do you think this will work by transfering my data to anew mac via firewire? I have read that resetting the pram may help so will give that a try.
Any help in laymans terms would be great. Really dont want to give a data recovery company £160 to save my stuff when the problem could be staring me in the face.

Sounds like a hard drive on it's way to hard drive heaven.

Sometimes booting into safe mode will allow you time to get your stuff off the drive, sometimes not.

At this point, pretty much no matter how you access the drive, it's going to lock up your system as it makes the attempt.

I would quit running any repairs to the drive, once they hit this type of operation, they just continually get worse.
I'd also quit using it and make your plans whether to get another drive or another machine and then try to salvage what you can.

And for those reading this - backup...backup...backup.

hard drive on its way to hard drive heaven?

Many thanks for your reply!
You have confirmed my suspicions. Do you think that target mode will work if I get another mac since currently it does boot into target mode? Also, do you think that my external lacie drive and dvd writer will be ok with another mac or will my imac have somehow corrupted them since they currently will not mount?
I am just a bit scared that hooking up my dying mac to a lovely new shiny one will somehow corrupt the new one. If you think that target mode is a good idea then I will go down that route. Although I will be very disappointed to say goodbye to my beloved imac, I would be over the moon to save my photos. If it works I will certainly heed your warning in the future and backup - backup - backup!