Window fashions on the slider.
Sheer grey w undertones of brown would be so pretty.
Check out the Luminette modern draperies by HunterDouglas.

Those are windows behind the couch, not sliding doors, I cannot remove the ugly verticals bc we are renting, do you still think those kind of drapes would work?

I had those dated blinds in my last apartment...open them up all the way so they will hide behind simple, straight hanging, accent colored curtain panels (add some toss pillows that coordinate)...mount inexpensive bamboo or matchstick shades beneath the curtains...this will add a nice texture into the space. the area rug beneath coffee table is much too small, especially in a space that you can't paint to add some color. maybe you can use it in the entry? remember, all elements of seating should at least have the front feet on or touching the rug to ground and define the seating area, and should work with the dark browns and the accent color of the curtain panels. and add some wall art...large art prints in a good frame are easy on the budget (art.com!!) just be sure you love the pieces you hang and that they work within your palette. table and floor lamps with the same shade (i love white drum shaped shades!) and maybe add a non-matching chair to set beside the TV to face the sofa.