Moving Hardrive From Old Computer

If I move my hardrive over from my old p6803w will my operating system come with it.

Also (IMPORTANT). My p6803w is running really crappy right now, therefore; my dad is worried if I move it to my new computer, even though I'm going to have an aditional 1TB hardrive in the new computer, that it will keep the new computer from running at it's full potential. He thinks that the problems from my old computer will just move onto my new computer. Is this true? If it is I will have to buy a new operating system

well big chance if you buy a new mobo and hardware that  windows will not boot anymore and result in a bsod ☺ so i will recommend a clean install anyway.

but if you do buy a 1TB drive, then just install the os on the new drive, because the new drive will probably be also faster. you can use the old one for extra storrage if you like. you probably need a clean install anyway.