Ok here is what i've was able to come up with to ask close to the spec that you've requested.
Although i will mention 2 thing,
1st, I could not find a way to fit any pentium dual-core cpu's with the price range you requested. What i could do how ever, was get a 2.6 GHz dual core Celeron cpu and that brings the price down.
Although it should still handle what your asking it to do. Now if the specs im seeing are true, then it basically like my pentium dual core laptop cpu (1.86 GHz, t2390) but just overclocked. With this laptop, i'm able to do mainy thing including light to moderate gaming. So i would imagine that it will handle everything your throwing at it just fine.
2nd, while i was able to fit the 450W PSU in the budget..... Im unsure of the quality as I've never heard of COOLMAX before. (maybe the guys in the PSU section of the forums could give a little more info about them)
For me, what i would normally recommend out the psu's, Antec, Corsair, silverstone, ect,. The cheapest psu to those quality is about $15 more (or factoring mail in rebate, it's only $5 more) for 430w corsair PSU.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139017
So if you wanted a slightly better quality psu, i would definitely recommend that.
Now on the list.
■$20.99 dvd Burner:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139017
■$19.99 Case:
http://www.newegg.com/Product/Product.aspx?Item=N82E16811154095
■$38.99 Hard Drive:
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136771
■$29.99 Power supply: $29.99
http://www.newegg.com/Product/Product.aspx?Item=N82E16817159065
■$21.99 ram:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820148149
■$50.99 Motherboard:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813130556
■$49.99 cpu:
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116348
Sub Total: $232.93
Shipping: $16.76
Total: $249.69
Yeah, it was close to going over but i manage to squeeze it in.
Now, this doesn't include any software in terms of OS or windows word, but it sounds like you may already have that. If you dont then that going to have to be an addition on to what's already here.
Hope this list and the Info i've giving helps.