Well it comes down to this. You want something that is impossible for your budget. You say you want to play the latest games top notch, well you cant do that any where near 500. If you built, or had it assembled by ibuypower or an equivalent then you would get more performance for your money then any store bought brand name pc, but you still, will NOT be able to play the latest games maxed. Perhaps if your lucky mid way with a lower res. If your wanting to max out newer games at a decent res your looking at 800+ with fairly low frame rates depending on the res.
If you don't know what parts to select at something like ibuypower, take a look at this chart, it is a pretty darn good computer for the money, but is over your budget, but will be massive leaps and bounds better for gaming.
Putting together a computer on ibuypower or another site is not building one, but it is still cheaper for the most part. You simply select the parts you want in it, and you can just choose these if you don't want to be creative.
Source:
How to Build an Awesome Gaming PC for $647 | Maximum PC
Keep in mind that these prices will be higher if you go through a company like IBP, so you are probably looking at more like 700-750. Which some of these things can be very much scaled down, the chart was just an example. another lower end gpu could be subsidized for the 5770 in the parts listed to lower costs. However the only thing i would consider scaling down in that computer would be the gpu, as lowering anything else is getting to the point where you really don't have a gaming computer.
The psu from the alienware computer could suffice, but we would have to know the specs of it, and the brand to know for sure. But if your doing that it is basically like building a computer, you have to completely unplug most of everything, and then hook the new one back up to everything. So if you are certain that you would not be comfortable building a computer then you will definitely not be comfortable changing the psu, nor putting a new gpu in. Even though these tasks seem daunting, they are in fact very simple.
To get a decent gaming computer out of a prebuilt then you are going to have to spend a fair penny, more then you would if you do what i and others have suggested. As most prebuilts are not meant for gaming, they are meant for businesses or family house holds. A lot of prebuilt brands such as alienware (which i would never, ever, advise someone to get a computer from them) offer gaming computers at a very premium price.