If your Xbox 360 is not playing though the Xbox One, this is what you should do, to find and, hopefully remove, the problem.
Test the Xbox 360
Plug the HDMI into your television and see if it works. Try the same cable, first, and the cable used on your Xbox One if it still doesn't work.
If the Xbox works without swapping the cables, everything on the 360 side is O.K.
If you have to change cables, your issue is with the HDMI cable. Try the new cable in your Xbox One.
Test the HDMI in on your Xbox One
Try connecting a different device to your Xbox One. A blu-ray player, your computer, even a set top box is fine (as long as you have HDMI out).
If other devices don't work, you may have a faulty HDMI in port.
If these tests are inconclusive
If the fault has not been found, you may simply need a better quality cable.
Quality does not make as much of a difference with HDMI as it did with component. You are always going to get next to perfect quality - if it works.
Some devices need a bit more power in the cable. Try a cable rated for 4K. Look for gold tips if you want to be sure. "Braided cable" does not improve quality. It just makes the cable less likely to break under strain.
I hope you find your solution here. I can personally vouch for cheap cable, here. The cable I am using cost me ten bucks, and it cost the store $2.
Best Answer
There's a comprehensive list on this XBox forum, for example:
As you can see two of the error states aren't particularly informative in and of themselves. You have to use the secondary error codes to determine exactly what's wrong.
As well as varying combinations of flashing red lights (known as the Red Ring of Death or RRoD) there are secondary error codes you can obtain from the console - assuming that you can get your console that far.
This Microsoft Support page details the steps to take if you get three red lights (the top right one isn't lit). The problem may be the console itself or the power supply. This page is an interactive guide to determine exactly what the error is from the lights that are flashing.