Well well well then... Let's see what I can recommend...
CPU: If your not going to be OCing AT ALL and your sure your not even going to look into it a tiny bit, then go with an i5 2400.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115074
It suits your needs and won't bottle-neck the video card. Really great processor but... Learning to OC is really, really worth it. It will speed your PC up and allows for more flexibility. It really isn't so hard. So, I do recommend getting an i5 2500k for $10 less at MicroCenter (it's also 0.3 GHz higher stock clocked).
http://www.microcenter.com/single_product_results.phtml?product_id=0354589 (beware, MicroCenter site is EXTREMELY slow).
Motherboard: You said you wanted SLI/CrossFire and that is a very good idea. It allows for future upgrades and just makes it more flexible in terms of what you want to do with it. I would grab a Gigabyte Z68 board.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128502
Gigabyte is one of the top motherboard manufacturers and Z68 boards, like this one, usually have more features due to Z68 being a newer and more advanced version of, say, P67.
Video Card: I really would save yourself about $100ish on the video card and grab a gtx 570 opposed to getting a gtx 580.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130595
There is no significant difference in terms of performance and the small amount of performance increase you get in the gtx 580 just isn't worth $100. The gtx 570 is most likely the most popular video card for gamin enthusiasts. Also, EVGA is a great company to buy it from. Rated #1 as a video card manufacturer, it really is worth getting it from them. This exact version is safely factory OCed, so you'll be getting faster speeds. Also, EVGA has a great Step-Up program. If you register your card within a month of getting it then for 3 months you have the choice of sending the card back in and simply paying the difference for a better card. I love it.
RAM: Easy enough choice. 8gb is more than enough to game, but I'm not sure if video editing requires a lot of RAM. Either way, more RAM is usually not better. It's the speeds that matter. Personally, I prefer it to be clocked at 1600 MHz which is one step up from 1333 Mhz (the lowest clock you'll see on DDR3 RAM, but also the standard). It really hits the sweet spot in terms of price to performance.
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231416
The company doesn't matter too much. G.Skill has always served me nicely.
PSU: Hmm well, considering you don't have too much of a limit on your budget, I would go for an 850w 80 plus certified PSU. Just saying here, an OCed i7 2600k with a pair of GTX 580's in SLI, an SSD, a hard drive, and 16 gigs of RAM will run about 525w from the wall on full load. This PSU will last a long, long time.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139011
80 plus certified simply means that the PSU is very efficient and is of good quality. Also, this PSU is made by Corsair, the leading PSU manufacturer (although they may be tying with SeaSonic and others argue that SeaSonic is better, but that doesn't matter much. It's a very good quality PSU.) I tend to stick with what I know and Corsair products (ANY of them) have not let me down. You might want to take a look at their site. They make very good products.
Hard Drive: Well, recently hard drive prices have shot up due to the flooding in Thailand. And although many of the factories there have recovered, the hard drive prices are still up there. Their prices will go down but that will be in a few months, so you might as well grab a good quality 1TB hard drive right now.
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136284
... Wow, they went up again. That hard drive used to hover around $115-140... Well, I still think it's worth getting. A very good quality hard drive, the WD Caviar Black is one of the highest end 7200 RPM hard drive there is. In fact, I would say it is the highest end. It should last you quite a while and is quite quick.
DVD Burner: Just grab any bulk DVD Burner. I have this Asus one and it works fine. They don't have much difference in them so it doesn't really matter which company you get these from.
http://www.newegg.com/Product/Product.aspx?Item=N82E16827135204
If you want BluRay, I recommend this one.
http://www.newegg.com/Product/Product.aspx?Item=N82E16827135247
Case: Now lastly, the case. Cases really are up to personal opinion and preference. Some people like a certain style. Others like another style. They do vary in features though. Now, I'm not exactly a fanboy of Corsair but I've looked at and have reviewed several of their products and I can't find that many bad things to say about them and cases is just one of the things that Corsair excels at the most. The 600T, in my opinion, is a very good-looking case. But fact remains fact that it is simply FILLED with features. It's got removable dust filters, tool free bays, tool free hard drive bays, very good fans, a fan controller, room to place a 120mm radiator, capable of supporting MANY fans, etc. etc. I could keep on going. And although I don't have this particular case, I am going to be ordering it in the next week or so.
http://www.newegg.com/Product/Product.aspx?Item=N82E16811139005
Oh and this is the white version of it. There is a black version but, unlike the black one, this white one has a side panel with a window included (as well as another with mesh.
Additional Thoughts: Forgive me I looked as though I were an advertisement on certain items. I simply tend to do that when I'm trying to recommend someone something. Also, keep in mind that Newegg is NOT in any way the cheapest site for computer parts out there (though if you know how and where to look, you can get some very cheap deals with rebates, etc. I'm just not a fan of mail-in rebates, though). If you head over to a nearby MicroCenter (if there is one near you) you can write down a lost of the items you want and just look around. They can have some really great combo deals and they do price their processors the cheapest (that I know) out of any other major company/store. I really hoped this helped. If you have any questions, feel free to ask and I'll give them my best shot.
-Neutral
EDIT: Wow, that took me quite awhile to type xD
EDIT #2: Oh and sorry for not listing the prices... got carried away
Hope you don't mind. It's definitely well within your budget though.
Facebook
Twitter
Instagram