Please Help me with the PC build.

Where do you plan to buy your stuff from?
Online or local retailers?
That's a very very tight budget especially if you include a monitor, HDD, GPU and PSU.
Extremely tight.
Suggestion would be to get it from the grey market... a C2D complete with monitor, mobo, HDD, case, keyboard , mouse is something like 22K .... which leaves you with 5K, wait for a month or two and collect some more dough say upto 8K and buy yourself a GPU that'll last longer into the future.... That ought to work out fine.

OK, you need a:
i3 3220:http://www.amazon.co.uk/Intel-3-30GHz-Graphics-Advanced-Extensions/dp/B008F65MO0/ref=sr_1_1?ie=UTF8&qid=1382180768&sr=8-1&keywords=i3
AMD Radeon HD 6670: http://www.amazon.co.uk/XFX-Radeon-6670-GDDR3-Graphics/dp/B00BJ2NOXS/ref=sr_1_2?ie=UTF8&qid=1382181072&sr=8-2&keywords=6670
500W PSU : http://www.amazon.co.uk/Corsair-Builder-Series-Bronze-Supply/dp/B009RMP2VE/ref=sr_1_1?ie=UTF8&qid=1382180804&sr=8-1&keywords=500w+psu
8gb RAM 1600MHz CL9: http://www.amazon.co.uk/Corsair-CMX8GX3M2B1600C9-Performance-Desktop-Memory/dp/B005G9C4K4/ref=sr_1_2?ie=UTF8&qid=1382180821&sr=8-2&keywords=8gb+RAM
Motherboard: http://www.amazon.co.uk/Gigabyte-XKT-1155-Z68AP-D3-Motherboard-Rev/dp/B0054X4I4M/ref=sr_1_11?ie=UTF8&qid=1382180848&sr=8-11&keywords=1155+motherboard
and you can choose the case

That all adds up to around £300. Which is around $485 USD.

Try this combination.... the game GTA V game will work fine on these as per
http://www.game-debate.com/games/index.php?g_id=1308&game=Grand%20Theft%20Auto%20V

Processor:
A8 or A10
http://www.primeabgb.com/amd-a10-6800k-richland-4-1ghz-apu-processor.html 9750.00
http://www.primeabgb.com/amd-a8-6600k-richland-3-9ghz-apu-processor.html 8300.00

Mobo:
http://www.primeabgb.com/asrock-fm2a85x-extreme6-motherboard.html 9399.00
http://www.primeabgb.com/msi-fm2-a85xa-g43-atx-amd-motherboard.html 6900.00

Ram: 8Gb
http://www.primeabgb.com/corsair-vengeance-8gb-1600mhz-ram-cmz8gbx3m1a1600c10.html 5199.00

HDD:
http://www.primeabgb.com/western-digital-caviar-green-wd10ezrx-1-tb-hard-disk.html 4149.00
http://www.primeabgb.com/western-digital-green-wd20earx-2tb-64mb.html 6050.00


Cabinet:
http://www.primeabgb.com/antec-x1-gaming-cabinet-front-red-led.html 2500.00

Now this is something that you need to see and figure out for yourself, the form factor needed is ATX and depending on the emphasis you put personally on looks and functionality you ought to set the budget for your cabinet, keep in mind the Air circulation and whether the room this rig is going to sit in is Air-conditioned or not..... there are a variety of cabinets available from maybe 1000 INR with a cheap PSU to 50K without a PSU....


PSU:
http://www.primeabgb.com/corsair-enthusiast-series-tx650-v2-power-supply.html 6049.00

Although 650 watts maybe a little too much for this rig, but, for future preferences if you ever plan or need to put in a GPU this will suffice for atleast the next few upgrades...

SO, it all works out to.....

8.3k+6.9K+5.2K +4.2K+2.5K
That's 27048.00 without the PSU.

http://www.primeabgb.com/corsair-cmpsu-vs650-power-supply.html 4157.00

Now those 2 PSUs are what I could find on the website go for the 6K one and you overshoot your budget like mad
Go for the 4K one and you still overshoot the budget
BUT

These prices are all bargain-able from wherever you buy the stuff.... so things could work out cheaper and you'd still manage the rig...

That's all I can help you with here.....
You can cut 8GB RAM to 4GB RAM... but...


PS:
Just got an update from my Grey Market chap.... you must remember that the price he quoted to me has 2K extra in it.... so
The cost of a C2D with 8GB of RAM, 1TB HDD, Cabinet,PSU Mobo, made by a grey market guy is selling for 16500.00 without the monitor, keyboard, mouse or DVD writer. The mobo has a PCIe Express Slot on it....

The Core i3 with the same config is for 22650.00......

Now, that get's me back to my first answer..... it would be well worth it if you went in for a buy from the grey market and added a good GPU with the money saved.

It ought to... the specs seem to be on the borderline , and the minimum requirement for the game don't seem to have anything actually that certain.... it's all a game of prediction.... what is available and what is expected.

Yup....