PLEASE help! Is it dead?!? Frozen PS3 no signal

So I got this console second hand. Did a factory reset and re-updated the software once I brought it home. It was working great for about 2 weeks, then suddenly, while using an in-game menu, the screen froze, purple and green blotches appeared and the controller stopped responding. I tried to press the power button but it would not shut off, so I unplugged it. (I know, I know, live and learn). Anyway, when I tried it again it worked for a moment and then froze again. This time I went online and learned to hold down the power button. The next time I turned it on, the TV got no signal, and the controllers won't connect. Still the only way to turn it off is with the long press. I have tried the reset (holding down the power button until the double beep). HDMI cable works fine with my other devices so it's not that. I'm hoping someone can help me because I'd really like to not spend much on it.