I am at the end of my tether with this, but want to try to have a healthy conversation about it rather than ranting at him (which is very tempting!)
DH works nightshifts, week on, week off. We barely see him on the weeks he's working as it's long hours + long commute. He's home about an hour in the morning, which he spends eating and on the internet. Then after he's slept he's here for about half an hour - shower, eat, run out of the door. It's pretty tiring for both of us, we have 2 DCs, 3 & 1 so pretty hectic everyday for me, and obviously tiring job and commute for him.
His weeks off are getting quite bad now. The first few days he's (understandably) tired, quite grumpy and can't do much. I know he must be shattered so am sympathetic to him. However, he spends pretty much every possible minute on the internet. He will wake up with the kids and let me have a lie in while he sorts out their breakfast, then he'll be straight on the internet. He'll make them lunch, but straight back on the internet after that. I ask him to play with the kids while I cook dinner and yep, he'll be on the internet 
This really got to me last week, as I had to listen to DC1 ask him 3 times if he could watch his Pingu DVD, every time my DH ignored him (of course, he was on the internet). DC1 ran over to me to ask me and I said loudly and pointedly "Try asking your father!" and he seemed to get the hint. Same week, I walked downstairs to see DC1 shove DC2, DC2 in tears, DH on the internet with his back to them (in a very small room, so no way he didn't hear/know) completely ignoring the whole thing. I walked over and turned off the modem as I was so sick of it. He must have noticed as he'd turned it back on after 30 mins or so, but he never said a word to me.
I've asked him to put the laptop away and play with the kids, but he never does. He'll change nappies, do their bathtime and bedtime, but I never see him just playing with them. They love him to bits but they've learnt not to bother engaging with him when he's on the laptop as they know they'll get no response. I think that is totally unacceptable, and my heart breaks for them.
I'm at a loss for how to breach this without sounding aggressive/nagging (though I think I'm within my rights to nag here!) as he will get upset, and start ignoring me. I'm not very well and don't want to have to cope with being left on my own with the kids again, while he has a sulk 
When I've bought it up before, he says I'm just as bad. I'm not. I do use the laptop for the odd half hour if he's down here and I think he'll play with the kids, but then he just generally gets his guitar out/does housework and still doesn't play with them. I can't use the laptop when the kids are around as they pull my hands off it, slam it shut - also I don't want to as playing with them is fun, and I'm busy enough at home, there's no way I could sit on the internet all day even if I wanted to, but he seems to think this is what I do
I've explained to him that I don't, and the kids wouldn't let me anyway, they only let him get away with it because they know he ignores them.
I'm so exhausted with this, as the week he's working they only talk to /rely on me, then the week he's here, they still ask me, follow me, want me (I'm happy with that as they're awesome, but it is exhausting, especially when I'm just seeing him on the laptop so much!) DC1 hasn't been sleeping very well and I'm shattered, which is making me a grumpy parent sometimes which I hate. On his week off he never takes the 2 out together (will sometimes take just one, but usually wants us all to go out together). If he's really tired I try to take both out so he can get some rest. I don't like going out to relax as I think they'll just get ignored while he's on the laptop. Same if I have a lie in/much needed nap.
Is there a calm, effective way to deal with this? I'm sure most people will feel like me and just want to rant and shove the bloody laptop up his bum, but I really want to try to deal with this rationally and not have it end up in a fight..