How to replace power supply Imac duel core intel flat pannel

That sounds like a heating issue. I would pull the back cover and make sure the small fan moves freely. Get a bottle of CLEAN air and blow it out. Otherwise...I have no idea.

Semper Fi,
Z

check power supply, check keyboard connection, check power to outlet, could be power cord, power button etc...

Hold the c key while booting to boot from a CD.

Checking the power supply isn't the easiest thing to do, it involves pulling apart the entire machine.
You can try resetting the SMC, unplugging all power, hold the power button for 5 seconds, replace power, then attempt to turn on.
if it still won't turn on, and assuming you didn't get AppleCare or it is expired (past 3 years) it might be worth taking in to an Authorized Apple Repair Facility and see if they will check it out for free. If it is under warranty, most definitely take it in or call 1-800-APL-CARE
If neither of those are an option, Power Supply http://www.ifixit.com/Apple-Parts/iMac-Intel-24-Inch-2-4-2-8-GHz-or-3-06-EMC-No-2211-GHz-Power-Supply/IF169-002
a tear down from iFixit for the 20" model, it is most likely very similar for your model as well http://www.ifixit.com/Guide/Repair/Installing-iMac-Intel-20-Inch-EMC-2133-and-2210-Power-Supply/1006/1
Hopefully that helps. Good Luck

And the problem is?
I'm guessing that nothing comes up on the second screen.
Go to system preferences, displays and you should see your second screen there, ready to be configured.

Power supply would be the best bet.

Possibly, the newer G5 Imacs feature Intel 2 Core Duo Processers. While older generations, do not support Intel Core Duo or Intel 2 Core Duo Processers.

It sounds like the unit has an optical drive failure, and most likely the drive will need to be replace

The most common problem with imac G4/800's are failing logic-boards. This will cause the mac to not power up at all giving the impression that the PSU is broken. 
If however, you are indeed certain that the fault is with the power supply, they are available from many stores online
Power Supply for iMac G4 15" LCD (700 & 800 Mhz) 661-3184 614-0147

A8V-MXs are built for AMD processors. You will need a board made for Intel processors if you want to purchase the above processor. If you want to stick with Intel and Asus check out the P5 series of boards. If not, buy an AMD chip...I've had AMD in almost every one of my computers, laptops and desktops.

Good luck.