Why won't my PS3 power on?

have a PS3, model number CECHB01, that I purchased used. I've had it over a year, and it worked fine for the first several months I had it. Then it shut down once while I was playing it. I let it sit for a little while in case it overheated, and the next time I played it a few days later the same thing happened. After several more days when I tried it, it would power on and load the game, only to shut down. There was no message or warning, it just turned off and the screen went black. Now it won't power on at all, and there are two red lights. When I press the power button, nothing happens. There are no flashing lights, and the two red lights remain the same. I have tried unplugging the power cable, switching the main power switch off and on, and even changing HDMI cables and ports, just in case something weird like that would help. I tried cleaning it, and that hasn't helped.

I don't know what else to do. I haven't been able to find anyone online with the exact same problem, but it's possible I'm not searching the right places or with the right terms. Some people had suggested for others with similar problems to change the PSU, but on one site someone recommended only doing that if there was no power to the PS3 at all. Since there's two lights, then that means it has power, right?

I'm not a huge player; I may play it for an hour or two here or there, so I don't think I caused it to overheat. I'd like to fix it or get it fixed. I don't want to buy another one, and I don't want to upgrade to the PS4 because I bought this one specifically because it was backwards compatible. Does anyone know of a way to fix it, or have any ideas or suggestions? I'd really appreciate it.