2011 27in Imac - randomly reboots

Question

I recently acquired a 2011 IMac 27in  ML 10.8
I really have two issues but they may be interconnected. The power button on the back seems to have moved. It is not exactly centered in the round opening. I am able to move it and it does power up when you hold it in. I also just added two more 2GB sticks for a new total of 8GB.
My worse problem is that after a while it will reboot itself. It doesnt seem to be connected to anything that i am doing at the time. Sometimes it has run a long time and other times only  a few minutes before it reboots.
So far I have:
1.Taken out the upgraded memory and gone back to the original2 sticks of Samsung 4 GB OEM. This didn't make any difference. Same result.
2. One of the forums suggested that it had something to do with Spotlight. I followed their suggestion and started a new index and nothing changed.
I don't think that this is a memory issue. My gut feeling is that it has to do with the reset button but that appears to work and boot on ok.
Any other ideas??
Thanks

Answer 1

If you have more than one user account, these instructions must be carried out as an administrator.
Triple-click anywhere in the line below on this page to select it:
syslog -k Sender kernel -k Message CReq 'GPU D|I/O' | tail | open -ef
Copy the selected text to the Clipboard (command-C).
Launch the Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Terminal in the icon grid.
Paste into the Terminal window (command-V).
The command may take a noticeable amount of time to run. Wait for a new line ending in a dollar sign (“$”) to appear.
A TextEdit window will open with the output of the command. Normally the window will be empty. If you get output like this:
kernel[0] <Debug>: disk0s2: I/O error
the boot drive is failing, or there's some other hardware fault in the storage subsystem.
If you get output like this:
kernel[0] <Debug>: ** GPU Debug Info Start **
kernel[0] <Debug>: ** GPU Debug Info End **
there's a fault in the graphics processor or logic board. The two kinds of output are not mutually exclusive, but if you get both, a logic-board fault is likely.