I also have had a hard time on Motz'ei Shabbos. Perhaps part of the problem is that, after a lengthy Shabbos nap, you have difficulty falling asleep (?).
There were countless times I did not want to go to friends' homes or go out at all becasue I said I was "too tired" or "too busy" or "did not have the time," only to then spend HOURS on the internet, later into the night than I would have ever stayed out!
In retrospect, i should have gone out with friends, I should have called someone and gotten involved in a conversation or an activity, or made plans, or just had a good time with friends.
Try that next motz'ei shabbos, connect with someone. Go to your local kosher pizza place and just have a slice or two, say hello to real people, INTERACT! It may make a big difference.
Can't hurt to try!
I also sometimes think that if my computer were on a timer, so that, especially motzei Shabbos, it just would not turn on, maybe that would help. Get a box, drill two holes in it. Put a timer on an extension cord and put it in the box (run the cord through the first hole). Put the computer cord through the other hole and knot it so you cannot pull it out. Set the timer so your computer only works from, say, 7:00 am until 10:00 pm. Then close the box, lock it and give the key to someone you trust, telling them it is only for emergencies. (You never know, in a real emergency (earthquake, terorrist attack etc (chas v'shalom!) you may really NEED the internet to communicate with friends and/or family).
Here is another idea: you probably have software that erases your tracks...remove it! As much as I have gone to places on my home computer that I am not proud of, I have never done it on my work computer, even the one I take home because...SOMEONE may see where I have been.
Don't feel bad that your Yiras Shamayim is not strong enough to stop you. It doesn’t mean you don’t have any. When Rav Yochanan Ben Zakai blessed his students before he died he said, "May your fear of heaven be equal to your fear of man". (The TaPhSiC Method) Use your fear of man to help you in your battles!
Chatzlachah rabbah!