How to wirelessly cast my PC screen to a non-smart TV?

Hey there,
just stumbled upon a topic I haven't seen yet. I'm trying to hook up my desktop PC to my TV (not a smart TV, just a regular one). Right now, I'm stuck using an HDMI cable. I really want to go wireless so I can move the PC out of my living room, but I still need to run all my apps and use the computer normally. Is that even possible? I've seen people mention Chromecast, but I have a feeling that won't actually work for what I need.
Any bright ideas?
Thanks!

So, why exactly have you got your PC hooked up to the TV—is it just for watching movies, or is there more to the setup? If you're mainly just looking to stream content, wouldn't it be much easier to just grab a dedicated streaming stick or a Chromecast instead?

I'm using my PC as my main hub for everything, including running IP TV through the TV screen, so I really need full wireless functionality to make it work smoothly.

Can't you just run a cable?

I could, but I'm actually looking to move my PC into another room, so I really need a wireless solution instead.