What Is The RDOD? Can I Fix It Myself?

I have an Xbox 360 Slim, I've had it for 5 years and 4 months and have never had any problems with it what so ever. So...I turned it on the other day, I played on it for about 20 minutes then it just completely froze and there were a bunch of grey lines all over the screen, I turned it off, left it off for several minutes and turned it back on, after about 10 seconds that red dot in the middle of the power button turned to solid red and every time I turn it on it makes a strange noise like something is trying to start but something else is preventing it from doing so. Does anyone know what is causing this problem? (Could the problem be that I always leave my Xbox on a shelf? Or because there were some storm issues about 4 days ago and the power to the whole house kept going out?) My warranty expired about 2 years ago so is it worth paying for it to be fixed or should I just buy a new one?! Any advice will be appreciated!