Nothing happens when I click the icon besides the program appearing in the taskbar for a few seconds.

My only suggestion is to get the version 1.13 mod. It's not the most simple way of doing things, but you can turn off any and all features you don't like that the mod adds by using the included INI file editor. You can also set the resolution and toggle windowed mode in the editor as well.

Jagged Alliance 2 should run on windows 10, 64 bits.

If however he refuses to launch, use "Stracciatella" which is a mod compatible with modern os and which is perfectly stable.

This mod is like 1.12 version (vanilla) of the game.

https://ja2-stracciatella.github.io