Is there a way of booting up a shut down computer since the power button does not respond-such as a command from the key board? The mouse and key board are wireless.

Short answer..... No.

Either the power button has gone bad (doubtful) or the Power Supply shorted out (most likely) not allowing it to turn on. Worse case scenario would be a Logic Board.

If you hold down the power for 10-15 seconds... does the light on the front of the iMac come on at all???

Try unplugging the iMac's power cord from the iMac (not the wall!) and count to 30 and then plug it back in. Attempt to power unit and let us know what happens.

In some machines, the PRAM battery is required to boot. Perhaps yours needs replacing?

iMac G5 - if Dave's procedure, doesn't help, then there's a good chance the system is dead. Which iMac G5 is it? The first two models were very unreliable and prone to freezes and power issues. You should take it to an Apple Store and have it looked at if it doesn't power up.

Jim is right in that it could be the PRAM battery, but being an iMac G5 I suspect it's more likely broken.

Many thank you for helping but I am going on vacation. I will be heading for the Apple store when I return with my First generation iMAC G5.

Can I at least save the hard drive which contains my forty movies and 6,500 songs plus I forgot how many photos? I do have most of them backed up on an external hard drive except the most recent they will be gone.

Could the fact that my back-up surge suppressor showed that I needed a new battery and since I have a whole house surge suppressor
I chose to remove the battery and plug back in? This when the computer would not boot up.

Have you tried plugging directly into the wall? Some of those battery backups don't work without a battery in them. Can you plug something else in to the battery backup and see if it works?

Along the same line of, "Is it plugged in?":

The connection between the line cord and the iMac body can sometimes come loose but still look fully engaged. Check this also.

Yes Yes Yes

A BIG APPLE AWARD to all that helped!!!

To me I say, "Why didn't I think of that?"

Should we understand that you now have a working computer?

What fixed the problem?

I replaced the surge suppressor.

LOL