Power Supply will need to be upgraded to at least 500 watts. This cuts deep into the $100 budget.
Here is a suggestion:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817438016 EVGA 500Watt PSU $37 after rebate.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130791 EVGA GeForce GT 620 $49 after rebate.
One of my friends has the GT 620 and it works well with games like WoW, Skyrim, GTA, etc... so it should be ok on "Normal" graphics settings to play the games you want, however not sure if it will play well on max settings, however its FAR better than the ATI Radeon 4200, so if the game is running in the Radeon 4200 now, it will be way better with this card! However this system would probably not boot and black screen on you if you try to get by with that 250 watt power supply! I have seen some people get lucky on a 350watt PSU and a video card similar to this one installed, but its running the powersupply to the max if it works at all and you are prone to crashes when the power supply cant keep up. So 500 watts or better is best.
I have one system that is running on a 460 watt power supply and a ATI Radeon HD5450 and I have to upgrade my power supply to install a better video card. Probably going to go with Corsair 650 watt because I have a higher end over clocked and power hungry video card that is going to be an upgrade for my system. nVidia claims that the video card I have requires a minimum of 500 watts, but its good to have more than less especially when you have extra fans and drives installed to draw more power from the system than a regular workstation build.