Did you already have some memory? I didn't see any memory on the links.
Depends on your brand and model of the computer. It'll be nice if you can open it up and take a picture of the inside of the computer for us, then we can point you to exactly what you need.
I wish Newegg makes the linking of wishlist easier. But anyway here it is for everyone to see: http://secure.newegg.com/WishList/PublicWishDetail.aspx?WishListNumber=14989526
Change out your Windows 7 32bit to 64bit. This one. Everything else looks pretty good.
Your CPU is fine for gaming. If you can shall out another $50 for the video card, I would go with the ATI 5770 card which is in the $150 range and will provide you with a lot more leg room for gaming performance. That's probably one component I would relax the budget on.
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2 things you can do to improve your build. First, get a power supply from a more reputable manufacturer, ie Antec, Corsair, Thermaltake, OCZ. I don't want you to trust your $600 computer on a junky $20 power supply. A bad power supply can kill your computer parts when they do spark or smoke...
Right, those are the only components you need to build a computer. As long as you choose parts that are compatible with each others (particularly the motherboard, CPU, and RAM), then you should be good to go. It'll be nice if you list or link us to the parts you wanna get, just in case. We can...
I would try taking the motherboard out of the case and see if it turns on fine that way. Make sure you don't have more motherboard standoffs than you need. You don't really need to reapply the thermal paste if you're going to remount the CPU fan, but better safe than sorry I suppose. I use 90%...
To be honest, I think that case looks to have pretty terrible airflow. There is no intake fan to direct cooler air from outside to inside the case. With only one case fan in the rear, it means it'll not have a uni-directional airflow, but instead air is moved from every gap and hole it can find...
That's a lot of questions. I'll try to tackle them one at a time.
There is really no difference in terms of performance between most of the 5770's. Mostly branding, engineering quality, tech support, and warranty separate these cards. XFX has double lifetime warranty which is the best...
Here's INCyr's working wishlist: http://secure.newegg.com/WishList/PublicWishDetail.aspx?WishListNumber=11058054
Ardrid gave some very good advice. I would recommend the ATI 5770 for video card as well for your budget and your need. You can certainly do very well with a 650W PSU, as pointed out.
You don't want to get the 32-bit Win 7. It still has a 4GB limit. Most of the time Win 7 32-bit will report 3.2GB usable RAM on any system with more than 4GB. Get the 64-bit instead, as it supports up to 16GB.
Ummm it's not bad, 5650 mobility is a fairly good portable GPU. If you may you should also consider these:
ASUS N71JQ-X1 NoteBook Intel Core i7 720QM(1.60GHz) 17.3" 4GB Memory DDR3 1066 500GB HDD 7200rpm DVD Super Multi ATI Mobility Radeon HD 5730
ASUS G Series G51JX-X1 NoteBook Intel Core...