is there any way to run Blender on the discontinued Intel 4 Series Express Chipset Family or will I have to fin
That is a very old Intel chipset. If you are asking about the integrated GPU (which is my assumption), the answer is, unfortunately, no.
According to https://www.blender.org/download/requirements/ you'll need a 4th gen Core i3/i5/i7 series (Haswell) CPU with integrated GPU or newer for Intel graphics.
Edit: The Intel 4 Series Express (Mobile) Chipset has the Intel GMA 4500MHD graphics hardware onboard. This is the same as the desktop GMA X4500 hardware, which is an OpenGL 2.0 card: https://www.techpowerup.com/gpu-specs/gma-x4500.c3140
If you really want to try blender, try a version before 2.76, as per the requirements page--it only needs up to OpenGL 1.4. Your performance will likely be terrible (slow clock speed, no dedicated VRAM, so it siphons some from your system) and you definitely will not get any CUDA support or any other fun things. Sorry!