Check the RAM with the Hardware Test CD, and try repairing permissions using Applications -> Utilities -> Disk Utility -> First Aid tab.
Also don't run any underpowered USB devices in the USB port nearest the modem port. That includes the keyboard, mouse, or any other USB device without an AC plug to the wall.
Do not attempt to run Norton Utilities, Disk Doctor, or Speed Disk. If have run Norton Utilities, trash it. It is what is causing your problems. Boot off the 10.2 Disk 1 CD, and run from the Installer menu the Disk Utility, and run First Aid's Repair Disk. If it finds problems, try repairing several times. If after 5 repairs it doesn't work, you'll want to backup your data to an external Firewire hard disk with Dantz Retrospect Express or Carbon Copy Cloner, and run Alsoft Disk Warrior on the iMac itself to fix the directory. As of the writing of this FAQ, Disk Warrior isn't available for Mac OS X, but hopefully will be available by April according to Alsoft's website. If you have a Flat Panel iMac that won't boot Mac OS 9 CDs, you'll want to reformat the internal hard disk after test booting your Firewire hard disk backup.
If after all this the problems are not fixed, take it to an Apple Authorized Service technician and tell them what you tried.
For spinning beachball issues, I recommend reading this FAQ: