Will this run COD 4?

Call of Duty 4 is VERY OPTIMIZED but it will run BADLY in a single core processor.

upgrade it to Pentium Dual Core, a very cheap dual core solution,
Intel Pentium Dual Core:
E2180-E4xxx SUCK
E5200-E5300, I'd pass
E5400 and above should be decent

Also, IMPORTANT, wat is ur motherboard?

So that I can find out if a PCI-express graphics card can fit in it.

Another possible problem is the RAM, 1 GB may not cut it; i'd suggest atleast 2 GB

and wat's ur budget too?

I know that it supports one x16 PCIe and one x1 PCIe card.
The motherboard is an Intel 925ex motherboard.
As far as budget is concerned, I'm not willing to spend top dollar. I'm looking for a cost-efficient solution that will run COD 4 smoothly.

Thanks.

oh man!
It seems ur motherboard can't support dual core processors; ur gonna need to buy a new one:
I suggest these items:

Motherboard:

GIGABYTE GA-G31M-ES2L(Newegg) 52 USD
I chose this motherboard, bcoz it has like around 500 positive reviews!

MSI G31TM-P21(newegg) 44.99 USD, this one is the cheapest solution in Newegg that has faily positive reviews.

NOTE: I'm sorry, I'm not very keen on AMD boards and AMD processors, so only Intel solutions there.

Processor:

Intel Pentium Dual Core E5400 @ 2.7 GHz (newegg) 69.99 USD
This is actually my processor and it should be sufficient for Call of Duty 4. Otherwise you can easily overclock it to 2.9 GHz or sumthing.

Intel Pentium Dual Core E6300 @ 2.8 GHz (newegg) 78.99 USD,
Choose this if u want a more fool-proof solution and/or don't wanna overclock!

NOTE: I'm sorry, I'm not very keen on AMD processors, so only Intel solutions there.

Videocard:

EVGA GeForce 9500 GT 1GB(newegg) 64.99 USD
my PALIT 9500 GT 512mb ran remarkably well with Call of Duty 4 paired with a lousy 2.00 GHZ dual core! I chose this one bcoz of the positive reviews!

Sapphire HD4670 512mb (newegg) 69.99 USD, although more expensive, its quite a bang for ur buck bcoz it runs almost twice as much as 9500 GT.

RAM:
ur new motherbaord will probably be DDR2, just get more RAM, atleast 2 GB which shud be around 54 USD

PSU:
Rosewill RD400-2-DB 400W(newegg)29.99 USD
Trust me, 400 watts shud do for wat ur buying

Case:
http://www.newegg.com/Product/Product.aspx?Item=N82E168... 14.99 USD

TOTAL: 278.95 USD if u chose the cheapest!

If ur really low on the budget, then go slowly...start with the videocard, then motherbaord, then processor; buying it one by one. If u happen to get satisfied by buying the video card alone; then thats good.