If the matter is as you describe, and you waste your time on the internet with things that are of no benefit, and that lead you to sin, by watching promiscuous programs and talking to non-mahram women, and sleeping and missing obligatory prayers, and neglecting your work, there is no good in your going on the internet, rather it is haraam for you to go online if the matter is as you describe. One of the basic principles of sharee’ah is to block the means that lead to evil; so every means that leads to something haraam is itself haraam.
What you have mentioned about how you are with the internet is a lesson to others who are take this matter lightly, and they give free rein to themselves, their families and their children, and do not wake up until it is too late.
We praise Allaah for having blessed you with a righteous wife who will remind you and help you to do good, and who has alerted you to the danger into which you have fallen. This question of yours points to the goodness that is in your heart, for the living heart is the one which is pained by the wounds of sin, as it is said: The dead feel no pain.
What you must do is hasten to repent to Allaah, and regret what you have done in the past. Give up the internet altogether, for time is the most precious thing that a man possesses, and the means that lead to haraam must be given up. Keep yourself busy with reading Qur’aan, attending lessons and keeping company with righteous people, and you will find that which will bring you happiness, joy, pleasure and peace of mind. No one sets right the relationship between himself and his Creator but all his affairs will be set straight. See also the answers to questions no. 26985 and 49670.
You should appreciate your wife and keep good company with her, and honour her more, because her sincere advice to you and her denouncing (your bad deed) indicates that her love is sincere, and that she is righteous and fears Allaah.
She has to carry on advising you, and help you to give up this sin, and keep away from it, so that your life together will be good.
We ask Allaah to guide you both.
And Allaah knows best.