My father denies that there is anything wrong with the computer and that a new graphics card will solve all the problems. He said that anyone that says otherwise doesn' know what they're talking about. He promised two months ago if I went to school and did alright, he would buy me a new computer. He then added that it could be any one that I wanted. He now denies that he ever said such a thing and refuses to buy a new computer. At this point I am not really sure what to do.
Your father is clearly inexperienced (no offense)... A new GPU won't magically solve the problems.
You need a new PSU first off to ensure the proper power output for the new components, unless you want an already outdated GPU as an "upgrade". If you want a new, recent GPU, you'll need more power - period.
After the PSU, yes, he's right about this, you'll need a new GPU. You'll also want a new CPU, so that no bottlenecking occurs. Because you'll need a new CPU, if you want one worth a damn, you'd need a motherboard upgrade, and at this point you may as well buy a new computer.
You could use a RAM upgrade, your specs say you have 6GB physical memory installed but it only reports 3GB available, either way you should consider upgrading to 2 x 4GB DDR3.
Sure, there's technically nothing "wrong" with your computer, but if you were to solely upgrade the GPU you run the risk of not having enough power, on top of that your other components would still be outdated and in the end you'd waste the GPUs potential due to the CPU being weak comparatively.
(yes I realize your dad is stubborn. yes I read your previous posts and am aware he thinks you have no idea what you're talking about. this post was aimed at educating *you* so you can take the steps to getting a better computer. try politely discussing it with him, or just google "bottlenecking" and show him that a new GPU isn't a magic fix-all solution)