Yeah, I kind of agree with most people so far. I feel like if you did want to start a business with this idea, it would most likely have to be a local business. Like everyone is saying, if all you are offering is parts and instructions, your clients would just as easily be able to do the slightest bit of research, and pick one of the Tom's best builds for a set price.
If they need instructions for assembly, not only will the parts they order come with extensive instructions contained in the owners manual, but they can also go to a detailed checklist, and get direct feedback from people on this forum.
The only successful way I see of running a business such as this would be to run this locally, and only charge people for assembly. You could offer advice on parts to buy, and offer to handle the entire assembly process, along with any returns necessary to wind up with a working pc. If you did this over the internet, as USAFRet said, there would have to be a point where money changes hands, and it would be very hard to find a happy place for both you and the client in this regard. For example, if they order their pc parts through your business, and you choose to keep the ordered parts, then they're out a bunch of money, and Cyber theft goes unchecked more often than physical theft. OR, if they decide once they get the PC that they aren't going to pay you, you're not getting your money.
A local business would work much better, in the fact that if the person ordered the parts and brought them into the store, if you decide to keep their parts, they can prove that you stole the parts much easier than they could online. Additionally, you could give a demonstration of the clients working PC in person so you can prove you gave them a functioning PC. If this was done online, you may send the client what you decided is a working pc and say it gets damaged in transit, then you have to deal with the customer not having a working pc.
However, I don't believe you would have a large enough client base if you did this locally, at least, not unless you expanded your business beyond exclusively gaming PC's. Not everyone is a PC gamer, and most that are just build their own computers, or buy a pre-built. There's not a huge number of people that are floating in-between these two areas.
Overall, a good idea in theory, but I think it would turn out to be bad in practice. If you wanted to run a business like this, my recommendation would be to look into starting a local PC repair company, and on the side, offer to build people gaming computers. I think jumping into what you're thinking of right off the bat would end up being way over your head, but if the business does well, it could potentially evolve into something closer to that.