It is possible to play Fallout 3 (and most likely FO:NV) on your PC with the Intel HD 4400 that is integrated into the the Core i3-4130.
I have a friend that was interested in playing Fallout 3 and Skyrim on his laptop which has a dual core i5-4200u and the integrated Intel HD 4400 and a 1080p screen. I have a similar laptop but with a dedicated Radeon HD 8850. I installed the games and setup the laptop to only use the Intel HD 4400 instead of the Radeon HD 8850 so that he could test out those games and decide for himself if the performance was good enough for him to buy the games.
Those games have a FalloutPref.ini / Skyrim.ini file that I edited to disable all shadows (the only way to do it) and decrease some texture sizes. The games were setup to have high quality textures, but everything else was low and I disabled anti-aliasing. Draw distances for actors was max out at 15, but I do not recall some of the other settings in the graphics option screen.
From what I remember, when playing at 1600x900 resolution Fallout 3 ran between 35 FPS - 50 FPS outdoors depending on the environment. Skyrim ran between 30 FPS - 45 FPS depending on the outdoors environment. At 1366x768 resolution performance was 10 FPS higher for both games from what I remember.
Fallout 3, FO:NV and Oblivion all used the same game engine; GameBryo; so your PC should be able to run all 3 games with similar tweaks. However, by default the GameBryo engine will not recognized Intel HD graphics. If you attempt to start a new game or load a saved game the game would immediately crash.
To actually play those games you need to use a custom d3d9.dll file that was originally created for the "Oldblivion Project". Oblivion was the 1st game to drop support for DirectX 8; the custom d3d9.dll file allowed people to play Oblivion with DirectX 8 cards instead of DirectX 9 cards. But since old DirectX 8 graphic cards lacked the hardware to run DirectX 9 effects. You can download the d3d9.dll file from the following site. All you really need to do is extract it to the main directory of the game where the exe file is located.
http://www.nexusmods.com/fallout3/mods/20371/?
While Fallout 4 uses an updated Creation Engine that was designed for Skyrim, you cannot play Fallout 4 using your Intel HD 4400. The game simply will not run. Intel will need to release new drivers that will allow the game to run.