Yes, post a floor plan and tell us something about your furniture. I'm having a bit of a problem visualizing the amount of room you have on each wall. We aren't professional decorators, but we know how to live small.

I suspect the TV is the most important factor for you. Living small wasn't going to let me get rid of the big TV either. But I did realize that my 5 year old elephant needed to find another home. I just bought a flat screen and cannot believe how much room there is now. Decided not to wall hang it, but I was able to get rid of the monster TV and furniture that was holding all. In your situation, wall hanging the TV may be a first step in freeing up area space.

You could mount the TV on the east wall if the air intake is located floor or ceiling heigth. I know the struggle that comes with the rest of the equipment, if the air intake is on the floor you could use furniture that has legs to hold the equipment, this would allow space below for the air flow.

If you have awful carpet and are not going to change it, pull it up along the wall and run the TV cable along the carpet strips to new TV placement. Don't pull carpet too far beyond the strips or you will have a tough time putting carpet back on. Sometimes these strips aren't right next to the wall, so you may be able to nest the cable between the strips and wall. Push carpet back and hammer back on. If carpet runs across a doorway/opening, just feed the wire under. I've done this in an office space, and it worked well without any issues with the carpet for 3 years.

Or, buy a large area rug...which would also be a solution to the bad carpet...run cable under the rug and duct tape it to carpet. Area rugs can be placed anywhere in your room and there are tons of options/prices. Laying one at an angle would give you even more length to work with for hiding the cable.

Also, try a search on TV decorating. There are a lot of photos available for ideas. Apartment living search might bring up a bunch too.