$400 budget can get you into a new Core i3 laptop with Intel HD Graphics which is a little better than what you have now. I saw that Best Buy had a pretty closely matched HP Brand A6 Processor Laptop for $229.99 last week for sale with 500GB HDD and 4GB RAM to your current troubled laptop. I ended up picking up a Dell Laptop for $279.99 with a 2.1Ghz Core i3 with Intel HD Graphics and its ok for gaming with lightweight games, or reduced graphics settings for larger titles like World of Warcraft etc.
$400 isnt much money for a "Gaming" budget and when it comes to Laptops the money is stretched far shorter than what you can get for a desktop computer. Reason being for a desktop system, you can take a low cost system and add a good video card to it in your own hardware combination. I have seen people stretch their money with desktop builds where they get a CPU that is not the most powerful out there and focus on the video card for starters in the new build and they get a Celeron, Pentium, or i3 CPU and pair it with a GTX nVidia video card, and this allows them to have a system that runs games that are not CPU intensive but are GPU intensive well. Then later on when their budget allows and if they find that the weaker CPU really needs to be swapped out for better they will buy a better i5 or i7 CPU. Same goes if going with AMD where you can get a low cost CPU, and later when budget allows get a better CPU.
My prior laptop I used for gaming before my Core i3 Dell is an ASUS Celeron 1000M Dual Core 1.8Ghz with Intel HD Graphics. I dont suggest a Celeron laptop for gaming, but just saying that I am able to run games on this older Celeron if I wanted to, its just that its slow for games to load, but once loaded they run ok on the lesser graphics settings for World of Warcraft for example. For a entry level gaming laptop a Core i3 is about safe for light weight games and games that the specs of teh laptop match up to the minimum specs to run the games. Some games that state they require a 2.4Ghz Intel or 2.5Ghz AMD Quadcore will run ok on a Dual Core CPU system but not all.
Laptops dont generally allow for easy CPU upgrades, and I dont suggest CPU upgrades of laptops, so when it comes to laptops, but buy it for what it is and leave it as it is unless adding memory if the laptop is able to be upgraded. Some max out at 4GB or 8GB RAM and become throw away computers when more is needed and more memory unable to be added. They do this by design so your forced to buy a new laptop sooner vs later if you want to do something that requires more memory.