450 dollars or less is like saying I need the cheapest one available, and those prices rarely come with any bigger screens than 13.3 inch and notebooks with that screen size are called "netbooks".
My opinion, just collect a bit more money so you can buy a decent notebook from a decent manufacturer.
http://shop.lenovo.com/us/en/laptops/th ... ries/e550/Just 100 dollars above your price, with a graphics card that could run minecraft easily and with a CPU that could survive Microsoft updates for a lot longer than the cheapest would do. Has 4gb of memory as well.
In the long run, this would be a much better investment. Computers don't get slower as they calculate just as fast as the day you bought them. However the updates that come over time make it bit by piece more heavier for the CPU causing you to think your PC is slow.
Sure you can go lower then 550 dollars, but that's all on you.
Edit:
You could also just reinstall your current computer with a different operating system.
Microsoft Windows is quite heavy on your system resources, installing software like
http://lubuntu.net/ could improve the performance of your current system, is able to run Minecraft and for office Ambiword and Gnumeric and for web browsing firefox could account for your "lightweight" needs.
Using this operating system could easily expand the usability of your notebook by a year or two. Oh, and its free! All of it.
