YouTube and Hulu flawless on HTPC?

You definitely don't need a video card to accomplish your goal, the built in video on Intel/AMD CPU's are perfectly fine for 1080p Youtube/Blu-ray videos.
As for building your own machine, it should be pretty easy to build a decent machine for $500, depending on if you need a copy Windows or not, which will make it a bit harder.
Take a look around at some of the other threads on here, there are plenty of recommendations for similar builds.

The Zbox you threw up should be fine. There is absolutely no reason why it wouldn't be doing 1080p YouTube or any other HD video you throw at it unless it was improperly configured.

Try installing the latest Flash player from Adobe, it allows hardware video acceleration.
If you are using Firefox in the Advanced->General tab , tick "Use Hardware Acceleration When Available"

His computer comes with amd E350 which I can confirm can't handle 1080p HD hulu/netflix.

Your internet speed also plays a significant role when Streaming

It works on a different computer so his Internet is fine.

The best thing to do is build your own.
Is the $500 just for Hardware? Or does that include the OS.
What storage do you need?
Other than Youtube/Hulu are there any other requirements?
Are you looking for something small like the Zbox? or something that matches your current equipment?

The best thing to do is pick a case that you want and then work around that.

Now is the perfect time to compile parts for an HTPC. If you are not already, make sure you are signed up for Newegg's newsletters for daily sales.

$500 is plenty for a powerful HTPC, whether you get dedicated graphics or not.

Here is a rough budget:

MB - micro ATX 1155 - ~$50 (AsRock, MSI, Asus, Gigabyte)
CPU - i3 - ~$100
RAM - 2x2GB 1600 - ~$20 (Newegg has a shellshocker today (12/17) on Ballistix 2x2 kit for $13.99)
OS - Win 7 Home Prem. - $80 (Win8 for $70 w/Newegg code: EMCJHJJ87 exp.12/17)
SSD - 120/128GB - ~$80 - $100 (Kingston SSDNow V+200 KR-S3020-3H 2.5" 120GB SATA III SSD $89 @ NE))
Case - $50

All this for ~ $400. (If you are patient you should have no problems getting quality components at the stated prices, and possibly even better)

See how the intel graphics hold up for you. I was skeptical myself, but I am satisfied with the HD2000 graphics in my i3-2120 HTPC.

If you want, you can always add a dedicated graphics card later, and still be under $500.

I built my HTPC last year at this time, and now putting the finishing touches on my server.
Edited by wiley165 - 12/17/12 at 9:06am

Yea, my HTPC is now 3 years old and I'm still using the old i3-540 Clarksdale with no separate video card and it plays 1080p Bluray rips at full quality just fine let alone Hulu, Netflix or YouTube.

 

Tip on Hulu, try Hulu Desktop.

Almost anything except for systems based on netbook parts aka atom or zacate. The cheapest possible parts are dual core SandyBridge celeron or pentium CPUs.

Lower end:

http://www.newegg.com/Product/Product.aspx?Item=N82E16819116409 $49

or

http://www.newegg.com/Product/Product.aspx?Item=N82E16819103951

Higher end:

http://www.newegg.com/Product/Product.aspx?Item=N82E16819113288

or

http://www.newegg.com/Product/Product.aspx?Item=N82E16819116774
Edited by jeffkro - 12/18/12 at 12:27pm

blu-ray is less system intensive then hulu or netflix HD.

Here's a sample of what the highest grade Intel HD graphics can do: http://www.youtube.com/watch?v=STCKwxzL3VM

I was talking about the Intel Zbox. Not the one he already has.

May be true but not really the point.  The point I was saying is a 3 year old i3 is plenty powerful enough to do HD streaming, BluRay, OTA, whatever you toss at it.  Thus it should be really cheap to build a system that can do Hulu.  ;)