Well, yes, last year I was in completely the same situation. My dh always played computer games, but when we got broadband, he started playing on-line, and it got to the stage where he would come home and want to put the pc on, and then play till four or five in the morning. Bearing in mind that we were both working, and I was getting up for dd in the night to find out that he was actually still awake and on the PC next door, this was not a tenable situation.
When I challenged him about it, he tried to cut down, but then I found out that he had someone else - he claims he met her through work, but I totally believe that he met her on line because she lives in the States. I am not for one minute suggesting that your dh is the same, but I do know that playing for hours on end makes someone tired, it doesn't make them a good father or husband, and it destroys your relationship.
There is a website called net addiction dot com, where you can do a quiz to see if you or your partner is addicted to being on-line. I have no idea how you resolve it (I did think about throwing the modem in the river, but in reality, he would have dived in after it).
I am now a single parent, and actually on some levels it is easier knowing that you are on your own, than having someone in the next room on a PC not being there to help you and support you (and your children) when you need it. I don't advocate it on an emotional level though.
I think if it is getting to the stage where your dh is on the pC on a Sunday instead of doing something with you and the children, you are right that you have a problem. If you can, I'd say that you need to keep talking to him and try to get to the bottom of why he is doing it, and what would make real life more attractive and the PC less attractive - when it came to the bit, I think my ex-dh's stress at work, the fact that he didn't want the responsiblity of children, and the fact that he felt he wasn't getting enough attention from me were all contributing factors. Again, I am not saying that this is the case with your dh, just that you need to find the strength to keep talking and to try and work out what is the root cause of this behaviour. Has he considered getting a less pressured job, for example, so he has more energy to do the things he loves? The PC is a means of escape, I think you are right, the key is working out (and changing) what he is escaping from.
I apologise for this long message, and I realise I may have written things you may not want to read. Do try and get him away from the PC in any way you can, days out, visiting friends and family, just try and get him back in touch with all the real life things other than work that he used to enjoy, and keep talking to him, that is all I can suggest.