Tested a repeatable problem with a new Gigabyte AMD RADEOPN HD 7870. After about 5-10minutes of gameplay in windowed mode my computer will turn off with no error messages and restart. 

The computer is not overheating as I have my eye on Hardware Moniter & Speedfan. Temperatures max out at worst 60celsius. 

While in full screen mode during the same games I have no issues.

I recently upgraded from a XFX AMD HD RADEON 4890 and this problem did not exist. The only new hardware in my computer is the 7870.

TIME FOR SOME SYSTEM SPECS!

AMD Catalyst Driver Version, and Driver History: GIGABYTE AMD RADEOPN HD 7870, Catalyst Version 12.10

Operating System: Windows 7 Home Premium 64-bit

Issue Details: Computer turns off while playing games in windowed mode

Motherboard or System Make & Model: ASUS PST WS Professional

Power Supply: Rocketfish 700w Model:RF-700wps2

Display Device(s) and Connection(s) Used:  Two LG Flatron w2361vg, 1 DVI, 1 HDMI

Applications and Games:

Games tested that turn off in windowed:

League of Legends, Eve Online

Games tested full screen that did not turn off the computer:

League of Legends, Eve Online, Metro 2033, Company of Heroes

CPU Details: Intel i7 920 2.67GHz

Motherboard BIOS Version: Version 6.1.7601 Service Pack 1 Build 7601 (msinfo32 works better than restarting)

System Memory Type & Amount: 12 GB Corsair

Additional Details: Memory check revealed no problems, no viruses, Latest windows update

Reformated and reinstalled Windows 7, and drivers. Problem still persists.

Continued Testing with Eve Online:

Everything freezing when windowed mode eve on right moniter and VLC or windows media player classic(cccp) on the left moniter.

Initial Problem persists and the computer turns off after 5-10mins of gameplay with Eve online Windowed on right moniter and nothing on left moniter.

Installed 12.11 Beta drivers

Problem still persists.

Computer turned off during window mode eve online 5-10mins.

Computer turned off during Full Screen mode after extended play of eve online 3 hours.

At this point I am out of ideas of how to solve this.

It's your PSU.   Complete garbage which cannot handle the power requirements of your system with the new card.

I'd recommend a Corsair TX650 or better.

Problem solved.

Replaced the power supply with a corsair 750w. The old psu was a 700w rocketfish with only the bad reviews it seems.

Thank you.