2006 Intel iMac not booting

Hello,

My 2006 Intel Duo 2.0mhz will not turn on. Late December, I unplugged it to rearrange my home office. When I went to start it up, nothing happened. I played around with pressing the power button for 5-10 seconds, then plugging in the power and turning it on. That worked, but after about 5 minutes the computer would just shut off. I tried resetting it a few times with the same result, until it wouldn't start at all. I gave up and it sat on the floor of my office for close to 3 months. I rearranged my office again in March, and thought I would try plugging it in again. This time it came up with no issues. I left it running until a month ago when I turned off the iMac to switch the power cable to a different outlet. When I went to turn it on, nothing happened. I tried unplugging it and pressing the power button for 5-10 seconds, then plugging it back in and tried to turn it on, but nothing is working this time. I even let it sit for a month without using it, then tried again without success. I am just trying to hold off as long as I can to see if Apple will release a newer iMac, hopefully soon.

Has anyone here had the same issue, and was able to fix it?