GeForce GT710 driver issues

How did you try to install the kernels?
Indeed, the graphical tool in Manjaro Settings, Kernels might not give back a detailed report on what failed.
Hence, please try to install the kernel packages from command line:

sudo pacman -Syyu
sudo pacman -S linux512
sudo pacman -S linux512-headers

Please post any error messages that might occur after issuing these commands.

As for your graphics card, it looks like it will be supported by driver version 418: Linux x64 (AMD64/EM64T) Display Driver | 418.56 | Linux 64-bit | NVIDIA (click “Supported Products”)

There are instructions on how to compile these drivers for Manjaro by yourself: [HowTo] Compile old/legacy NVIDIA Proprietary Drivers [2020-12-30 Update Issue]

But let’s see if you can get a more recent kernel installed first.