RROD?

This thread ought to have everything you need;
forums.xbox.com/.../71416.aspx

Might want to consider buying a new xbox if it's no longer under warranty.

You'll want to have your console
repaired. I suggest you
contact support and set up a repair. The phone number is 1-800-469-9269.

Its hard to find anything to help out as the Xbox 360 console is no longer supported, but i did find this here,

https://beta.support.xbox.com/help/xbox-360/store/flashing-lights-solution

That being an Xbox 360 slim model, the light codes that show up are a little different, they come up as a single flashing red light or a solid red light, which can be known as the Red Dot of Death ("RDoD") over the older Xbox 360 models, Red Ring of Death
("RRoD")

Also, might want to check the power supply unit ("power brick") lights, which i found here,

https://beta.support.xbox.com/help/xbox-360/console/check-power-supply

If you tried all the solution that you can try to solve this and the console still wont power on and it still show the red lights on the power button,

Am afraid that the console has most likely, well and truly expired.

For the age of the console, i would say that its not worth getting it repaired, because it will be like giving it a band aid and band aid's don't last very long, then you'll be back to square one with the same issues coming back more and more often,

I've had and gone through 12 Xbox 360's with "RRoD and RDoD", some I've had repaired in the past but the same issue kept coming back shortly after the repair, so its not really worth it.

I would lay it to rest and welcome in an Xbox One or wait until the end of this year and welcome in an Xbox Series X.

how are you enjoying skyrim??