What are you blind? If you were looking at the screen you would clearly see that Neo is not typing on his computer. How could he anyways if the computer was off?? I think that you made a slip-up.
He had just gotten into work and drilled out by the boss for being late, perhaps he needed some down time to refocus his thoughts before he started working, hence the computer not being turned on yet.
Um, he wasn't working on his computer. He was just sitting there staring at the blank (turned off) screen. Just because someone is sitting in front of a computer it doesn't mean he's "working."