First of all, Honeypot...I hope you are feeling MUCH better.
2nd....I really COMPLETELY understand why this could be a BIG problem for Mr.Doglover. I experience this with my LDH....he loves to relax by playing his computer games for hours on end. I get jealous of his time on the computer, because it's time he could/should be spending w/me because I feel alone, neglected, ignored etc....and that damned inanimate object gets more attention than me (at least that's how I used to feel).
I guess this one is just pretty cut and dry for me....if he thinks you spend too much time on the puter, you very well may...at least for now, in your R. If he views that computer as his competition (and that's what I did often) then that's not good. IMHO it's best to really pay attention to when you choose to check your e-mail, and monitor how much time you spend on the puter.
One thing that helps us is that I'll let my H know if there's a movie coming on....or if dinner will be ready...in a certain amount of time. This way he knows I want his attention at those times....I give him the time he needs to unwind a bit on the puter, and then he gives me my time too. So far it's really working well....but you know what? I'm noticing, he's spending MUCH less time on the computer and I haven't even asked him to....but he's choosing to do this because we are happier spending time with each other now...not apart from each other (but under the same roof).