Q: HOW CAN I START UP MY IMAC G5 IF THE PASSWORD HAS BEEN FORGOTTEN?

In your situation, without the Password, your only alternative, I believe is to boot from the Original Installation Disk in order to reset the Password.  You will need to obtain the correct disk somehow so I would suggest starting with contacting Apple to see if per chance they still have whatever version of OS X shipped with your iMac (10.3.x ?) and will sell it to you.  Otherwise you could try a place like eBay.

Hope this helps

I stand corrected.  I found the following article, which should hopefully solve your problem:

       http://gigaom.com/apple/reset-os-x-password-without-an-os-x-cd/

Hope this helps