How old are you? Focus on school and move out when you turn 18. While I don't think your mother handled things very well, it sounds to me like you might have been spending too much time playing video games. Work on finishing school instead, maybe do some extracurriculars or get a part-time job (or start a business!). Spend as much time out of the house as possible, study at the library etc. Being around your family as little as possible helps when you have a truly unstable family situation.
If you want to game, you could maybe get a gaming laptop instead, and keep it hidden from your mom...but when you live with family members, that has a strong possibility of not working out for you (they'll just find it eventually).
Your mom *should* replace your computer if you paid with it with your own money, but that's a whole other road to go down and unless you feel like taking your mom to court I'm not sure it's worth the emotional effort.