Blank screen while CPU runs fine or 'no signal' on monitor when

pc specs:

Processor: Intel 2nd gen core-i5 2400k 1.3 GHz
Motherboard: ASRock H61M/U3S3
Graphics: Sapphire Radeon HD 6870 1GB 256-bit GDDR5 PCI-E 2.1x16
Ram: G-Skill Ripjaws 4GB DDR3 1333
HDD: WD Blue 500GB 7200RPM
OS: Windows 7 Professional
owned pc since april 2012

initial problem:

Recently while playing a game my screen went blank. There was still power
in the monitor (as suggested by its backlight) and everything inside
the cpu was running fine. Then I restarted it. 4 out of 5 times the screen went blank right after the initial windows 7 (loading) screen. Then it stopped entirely. Even the bootscreen wouldn't show up and the monitor gave a 'no signal' message.

So after connecting and reconnecting the PCI express card and cleaning most of its dust the computer did start. But once again after a while the screen would go blank. Sometimes it'd happen during a game, sometimes while browsing the net or just by itself if left alone. The time varied. It could be 3 mins or 5 hours. In all those instances, only once did I see a blue screen (after pressing alt+f4 and ctrl alt del). But then it never appeared again. I changed monitors, cables but the same blank screen. I was even lucky to get a boot screen as most of the time that 'no signal' logo would show up.

I tried switching to on-board but for some reason the initial boot screen would show up and then restart itself after the screen with the blinking _ (underscore). This would repeat till PC is turned off.

Solutions tried (from the net):

Ram + ram slot cleaned
Power button pressed 2-3 times (with cables disconnected) to get rid of excess electricity
changed monitor
changed hdmi cable
tried DVI port

new development:

After some experimental methods, I found that holding the pci-e power cables into the gfx card power ports tightly caused the pc to run ok but the moment its released/grip loosened, that 'no signal' logo would come up. Tightening the
contact again produced no results. So I'm confused whether the problem is with the graphics card or the power supply.

Im actually running the pc now with a PCI express gfx card that doesnt require power. But strangely, now when I activate the on-board graphics from the bios, the computer doesnt restart. This is very weird since the hdmi cable is conected to the motherboard (not the card). Unplugging the gfx card causes the same restart cycle.

SO this is my question: is the problem with the power supply or the graphics card? Is there any solution you'd recommend or do I have to send it for warranty?