Under 500$ including OS

what is the computer going to be used for?

Mostly internet stuff, with some HD video and very mild gaming (I think intel HD 2/3000 would suffice)

well then

i3 2100
H61 mb
2 x2 gig of RAM
400 watt psu

cuts it really short on funding!
Ofcourse, there's always a $500 laptop, but if you want desktop items, $100 already go into the operating system (if you want Windows).

That leaves $400 for remaining parts.

For that money it's best to go with combo deals, or a preconfigured pc.
If you want all in one, you'll have to do with netbook speeds like this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Bump up the CPU to normal speeds, and we're talking about the $760 area.

Desktops under 500 (screen, keyb, and mouse excluded), you'll get last generation hardware, which really isn't all that bad; it was the newest 6months to 3/4 a year ago, and it's not like you won't be able to run latest games on it (all but perhaps a handful).

This one even comes with a keyboard and mouse, $509 but the $9 over the budget are well invested in the keyboard and mouse!
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

If you want to create your own desktop from parts,
Windows 7 costs $100.
Get a corei3 with integrated graphics, cheap SATA2 harddrive (upgradeable in the future)
Motherboard that supports USB3.0 ports, at least 4 or 8Gb of DDR3 2000 RAM memory (or faster), and a 450W powersupply.

You could also select a Linux OS (which is free), and saves you $100 for the initial setup, so you can invest in a better CPU (core i5), mobo (more feats) and PSU (500W, for later expansion with a plugin graphics card), and/or RAM speed (faster RAM only costs marginally more).
Only problem is, there's really not much you'll need a fast computer for in Linux.