do you have the money in your budget to build a new pc? Would you be comfortable putting tab A into slot B? Pre-built PC's are very rarely worth putting the money into to upgrade. After all is said and done you are 80% there to building a new pc with the power supply and GPU upgrade. It's already 4 years old, which is about the life expectancy of a pre-built pc before it really becomes limited, as you've found out.
OEM (Original Equipment Manufacturer) copies of Windows are tied to the motherboard. It may be stored on the HDD, but once you replace the mobo, as far as an OEM copy of Windows is concerned, it's on a new pc and is pirated.
PC's are pretty much modular. You plug parts together, follow a few simple instructions and cautions, ask questions if you are unsure (which you are doing) and it "usually" works.