Love your inspiration photo. I would start with painting the blue accent wall and paint the other walls the same color as your desktop since it's a small space. Mirrors and reflective surfaces will help make the room feel more expansive, so consider adding metallics and glass.

My concern is with the cool colors you're talking about in a basement with a very small window. You don't want this space to feel cool - do you want it to feel warm and inviting? When you say cozy, what exactly do you mean? Color has a psychological impact, so do keep that in mind. Years ago, I saw a college basement office, and it was about three times the size of this room. It was done in yellow with lots of plants and colorful wall prints. It had no windows, but with all the lovely warm decor, you'd never know it was in the basement. If you plan on keeping the current wall item, bring it down so when you are standing, the middle of it is at eye level. If you want to bring depth to this room, get a wall piece with a three dimensional quality to it. For example, in my condo there's a very small room where I have scenic prints where you can see for many miles in the distance with prairies or mountains. Keep in mind the concept of negative space. Every nook and cranny doesn't need to be covered. Let the eyes rest at some points in the room. Regarding the cabinet, if you are a neat freak, certainly get open shelving but if not, stick to a closed piece.

Do not start painting random walls dark colors. That's a big no. Keep the paint light and the same color as the rest of the basement to make it feel as big as possible and not segmenting it into even a smaller space separate from the rest of the larger basement. It's difficult to tell what is going on in that space with only that one picture, but from what I can see only, I would put the desk on the back wall where that little picture frame is now and make that wall the "focal point" of the "office".

Dark colors recede, but my concern would be that it’s too dark to work in, unless you really bump up the lighting. Your inspiration photo has a lot of natural light. I really love that color, too. Something about a deep, rich blue that is very attractive. The photo you like uses it as an accent wall, which really works in that scenario. In your situation, I’m afraid it may make the room seem unbalanced, with the color on one side.