[Help] $800 Build for a Friend

Well if you go ahead with selling him your i5-3750k this is the best you'll be able to do with his budget:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($189.99 @ Microcenter)
Motherboard: MSI Z77A-G41 ATX LGA1155 Motherboard ($69.99 @ Newegg)
Memory: G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory ($39.99 @ Newegg)
Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive ($55.99 @ NCIX US)
Video Card: HIS Radeon HD 7850 2GB Video Card ($189.99 @ Newegg)
Case: Antec Three Hundred Two ATX Mid Tower Case ($54.98 @ NCIX US)
Power Supply: Antec Neo Eco 520W 80 PLUS Certified ATX12V / EPS12V Power Supply ($46.98 @ Newegg)
Optical Drive: LG GH24NS90 DVD/CD Writer ($17.99 @ Amazon)
Monitor: Acer S220HQLAbd 21.5" Monitor ($119.99 @ Newegg)
Total: $785.89
(Prices include shipping, taxes, and discounts when available.)

The $117 with shipping Storm Scout isn't going to work with his budget.

This is the build I would recommend for an $800 budget:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($119.99 @ NCIX US)
Motherboard: ASRock H77M Micro ATX LGA1155 Motherboard ($69.99 @ Newegg)
Memory: G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory ($39.99 @ Newegg)
Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive ($55.99 @ NCIX US)
Video Card: Sapphire Radeon HD 7950 3GB Video Card ($289.99 @ Newegg)
Case: Antec Three Hundred Two ATX Mid Tower Case ($54.98 @ NCIX US)
Power Supply: Antec Neo Eco 520W 80 PLUS Certified ATX12V / EPS12V Power Supply ($46.98 @ Newegg)
Optical Drive: LG GH24NS90 DVD/CD Writer ($17.99 @ Amazon)
Monitor: Acer S220HQLAbd 21.5" Monitor ($119.99 @ Newegg)
Total: $815.89
(Prices include shipping, taxes, and discounts when available.)

There's a $10 off combo deal for the memory/motherboard that isn't reflected in that price.

Alternately you could downgrade the video card to a 7870 and go with the Storm Scout case if he's really got his heart set on it.

This is a very good question, and mostly my biggest dilemma when helping people do really tight budget builds.
If you're gonna purchase everything from Newegg, it has a good chance of altering the build due to difference on prices.

I really enjoy using newegg and have been a customer of theirs for quite some time. Thus they are my preference and I find it easier to order everything from the same place, but it is not entirely necessary.

I didn't say it was a bad thing.  
I find it convenient as well to to just order from one website.

I think lighter17 got just about as best as you can do with the i3 build - CPU is less important than GPU when it comes to gaming, and the i3 is a solid performer. If you're a bit miffed about putting a mATX board into a mid-tower, then you could opt for the Fractal Core 1000; you'd lose the space to have more than 1 hard drive, though, using the 7950. If you really need the price to be closer to $800, you could also ditch the optical drive and install Windows from a USB, if you've got an extra flash drive lying around (with backed-up or non-essential data, of course).

Other than that, everything is great. NCIX is right up there with Newegg in terms of respectability and reliability, so while it's less convenient to order from both, it'll save some money.

Edit: Thought I'd look through some of Newegg's combos to see if you couldn't save any more money. Found a few things you may be interested in.

ASRock H77M + 8GB Ripjaws for $10 less than separate (same mobo and memory from lighter's list)
i3-3220 + Rosewill Challenger for $16 off ($160 total) - the Challenger is not quite as nice as the Antec 302, but it's a bit more affordable.
i3-3220 + CM Storm Enforcer for $204 minus $25 in rebates, in case the chassis is really important to you (him) and you don't mind going over budget a little (this'll be $5 more than the i3/Antec after the rebate comes in; I don't recommend relying on that, though).

Thank you all. Input is much appreciated. I'm going to look it all over tomorrow and I'll post an update.

Thanks again.