Computer not working

I'm not sure if this is in the right area or not but I hope I can get some help with my problem.

I had this computer built 3 years ago and it's worked perfectly for everything I've wanted it for, but recently I've been having this problem; a few months ago I was playing one of my regular games "league of legends" when my screen flashed black but came back straight away. I ignored it and it happened again, increasing with frequency and duration until it would go black for minutes before coming back. I turned off my computer and left it for a few hours and it was fine again. The next week on the same day the exact same thing happened with the same solution. This happened for a few weeks until, suddenly, it stopped. Yesterday the problem happened again and I turned it off, 14 hours later I turned it back on and it was still acting up. I restart it and it won't turn on, the light on my power button flashed twice every 5 seconds and 2 beeps come out every time it flashed. I turned it off for a few hours and turned it on again, it worked for about 30 minutes then screwed up again. I've tried pulling it apart and cleaning it (the graphics card was caked in dust), restoring it to previous backups - up to a month ago, and it still won't work.
Does anyone know how I can fix this? I'm debating restoring it to factory settings but I risk losing 900GB of data, so I'm hoping to find a way around it.

These are the stats of my computer:
Intel BLKDH55HC H55/ATX/DDR3/LGA1156/PCIe2.0x16/GIGA LAN motherboard
Asus Radeon 5450, 1G, DDR3, PCIE2.0, DVI, HDCP, HDMI Graphics Card
Core i7 870/2.93GH/8MB Cache Processor
2gb DDR3 x2 Ram

EDIT: I've also tried it in safe mode but it still does messes up on me.