I bought my Lenovo Yoga 515-ISK in 2015 in Vietnam for $200 USD apx. I've been running Ubuntu Mate 16.04 as my operating system on it. My laptop looks very similar to yours.
It's not dead but I do want to get a new one when I can. I didn't do a lot of gaming on it. I hear gaming could wear out a computer out faster. My laptop uses Intel instead of AMD. Perhaps Intel does better sometimes.
I'm not sure as I sometimes hear good things about AMD. I do have a SSD for a hard drive and they say that is a bunch better than the older HDD types of hard drives with the mechanical parts inside. I do recommend solid-state drives because it seems not to deteriorate as fast.
I use HDMI to connect to my TV and it works. When you say matrix, I assume that has something to do with the graphics, the connection between your laptop and the TV. Maybe a type of hardware failure.
If any of your problems are absolutely or even partly software related, I would recommend lighter operating systems which might be able to give your laptop more life assuming it is possible to go lighter on it.
But of course it can be tough to learn a new operating system (OS) and figure out how to make it compatible to games, software, hardware, find drivers, etc.
after half a year problems with him started, and so I went for 6 years. In some time I have to invest in a laptop of some kind. It's a pity, but more and more it caused that everything was crashing and updating the graphics drivers broke the computer. I know that you can do a computer format, but the lack of a matrix (which I broke) eliminates because it can not be done with a laptop connected via HDMI to TV (I checked) My laptop crashed in 2015 hmm $ 420 so the price is very similar to yours. for me Lenobo is a failure in use
Perhaps it is partly or totally a fault of Lenovo, I think I've heard of some bad reviews regarding them over the years.