thats gonna be rough with all parts included, new copy of win7 and a reasonable monitor are going to cut your budget down horribly. I would recommend going with some used parts. Might be difficult to find but would make the machine worth having.
AMD build will probably save you the most money:
phenom x4 955 (new): $87
CM hyper 212 evo: $30 (after $5 MIR)
WD 1tb HDD 64mb cache: $65
Apevia X-dreamer Case (comes in multiple colors all same price main thing is includes all case fans side panel fan will need removed to fit hyper212 but allows room for lower 120mm fan):$65
Rosewill capstone PSU (amazing quality per dollar): $60
Geforce 650ti BOOST MSI TFIII: $155 (after $25 rebate card)
Gigabyte 990fxa-UD5: $150 (after $20 rebate card)
G.SKILL ripjaws X series 8gb (2x4gb): $70
So far thats all new parts at $682 (After rebates) and all come with decent reviews. I am not super familiar with what would be a good cheap monitor/mouse/keyboard. I do know with the keyboard you would much prefer a older mechanical keyboard that will last for years (newer mechanicals are usually fairly expensive). I dont think that it will all fit under that $800 mark you are looking for but It would be a decent rig for the cost. If you can find most of those same parts used (id stick with a new mobo/hard drive atleast prolly new psu too) you would probably be able to come under budget and still have a great machine.
Let us know what all you decide to use and how it works out
those sites they posted above are helpful, that AMD A8 system is a good budget build could easily be upgraded to the A10 as mentioned. Great resourceEdited by dmfree88 - 8/5/13 at 4:17pm