Why does my iMac just quit and it won't turn back on. Sometimes I can start it a few days later.

Question

It was working just fine and then it just quit. I tried turning it back on but it wouldn't work. Then like 3 days later, I tried turning it on and it came on and worked ok and just quit again.  Again, I tried turning it back on and again, it wouldn't come on. I tried again a few days later and it came on. What the heck is wrong with this computer?   It has Mac OS X 10.6.8 and the following is the info I got from profiler:
Model Name:                       iMac
Model Identifier:                   iMac4,1
Processor Name:                Intel Core Duo
Processor Speed:               2 GHz
Number of Processors:       1
Total Number of Cores:       2
L2 Cache:                             2 MB
Memory:                                2 GB
Bus Speed:                          667 MHz
Boot Rom Version:              IM41.0055.B08
SMC Version (system)       1.1f5
Serial Number (system)     QP********U2S
Hardware UUID                   00000000-0000-1000-8000-0016CB8BC90C
It had a program called deep freeze on it when I first obtained it. That program would not allow me to make any changes or save anything. A friend gave me a disk and I installed it and it took that program away. It was working fine and then as I said, just quit. I got the computer from an auction from a community college and deep freeze was the program they used to make sure the students using the computers couldn't change anything. When ever the computer got turned off, it would default back to factory settings. When it first turned off and wouldn't start again, I tried taking out one of the two memory sticks and it worked. I then went and bought two new memory sticks and installed them and it worked ok. Then it started doing the same thing again.

Answer 1

Hi codyfromchurchill falls,
Welcome to the Support Communities!  The resource below will provide some troubleshooting steps if your iPhone is unresponsive or won't turn on.
If your iPhone, iPad, or iPod touch doesn't respond or doesn't turn on - Apple Support
http://support.apple.com/en-us/HT201412
If you see a black screen
You might need to charge your device before it can turn on. Plug in your device and let it charge for at least 10 minutes (20 minutes for iPad), then try turning it on. 
You should see a battery icon while your device is charging. If you continue to see a black screen, reset your device. If your device doesn't respond when you press buttons
Your device might not return to the Home screen when you press the Home button, wake from sleep when you press the Sleep/Wake button, slide to unlock or power off, or it might appear frozen. Try these steps:
Restart your device.
If it still doesn't respond, or if it doesn't turn back on, reset your device.
If your device gets stuck during startup
When starting up, you might see the Apple logo or a red or blue screen for a long time, or your device might restart again. Try these steps:
Make sure that you have iTunes 12 or later on your computer.
Put your device in recovery mode.
When you get the option to restore or update, select Update. This will reinstall iOS without erasing your data.
Get more help
If you still need help after trying the steps above, contact Apple Support. 
Last Modified: Jan 14, 2015
I hope this information helps ....
- Judy