The more I look at it, the more I think you should open that valve. I spotted that it is connected to the mains, I didn't see the tap on the wall before.

I can't tell from your photos which pipe is which. What's the angled tap valve for on the wall? Is that the water mains inlet valve? It'll need filling under pressure, there will either be a valve which is already connected which needs opening, or a bridging tube which needs connecting first.

Or get a condenser tumble dryer, it doesn't need venting and any heat generated stays in your home.