Vordenator: Windows 8.1 64bit, Core i7, Radeon card.
Any suggestions didn't work for me, but then I tried DXWnd programme.
In Video tab I have "simulate 16BPP desktop", "Set 16BPP RGB565 encoding" and "Monitor native modes".
Heroes 4 runs very smoothly both in adventure and battle modes. In fullscreen.
THIS!
I can't believe after all these years, I'd get a perfect solution to this problem!
I just tried it with 7 creature stacks and there is zero lag! Oh my!!!
Here is what I followed.
Installed the game.
Installed the equilibris mod after replacing the two files as written in the instructions.
Installed DXWnd, followed the steps here:
https://www.play-old-pc-games.com/compatibility-tools/using-dxwnd/ After getting the game icon in the initial window,
Changed the exe path with the equilibris mod exe's path so that I can also use equilibris mod with this.
Changed windowed mode to fullscreen
(both under right click -> modify -> MAIN tab of DXWnd)
Smooth as Reese's buttercup.
But I guess I might play in windowed mode because fullscreen seems a little stretched for me.
EDIT: Can't play it in windowed mode, DXWnd shows black screen if I try that and then crashes. Fullscreen it is!
EDIT2: I tried the fullscreen mode on my work PC and it looks perfect without any stretching (black bars to the sides, the way I want it).It seems my home PC stretches the game window via graphics settings because that is the only difference between two PCs. I'll try to get those lovely black bars at home, and I'll report here if I find the solution.
LAST EDIT:
https://forums.geforce.com/default/topic/738809/i-can-t-change-aspect-ratio-on-nvidia-control-panel/ This link put the last piece of the puzzle and finally, after all these years, I can play this game with zero lag, fullscreen and without fullscreen stretching. The black bars stay either side so that the game graphics are finally as they are supposed to be.
I tried many things to have these black bars but nothing worked. Finally I read the last post of the link above, and then first changed my resolution from native 1920x1080 to 1650x1050 in Intel integrated graphics card driver. After I did this, a new option appeared on the screen which said keep width-height scaling. For some reason, this damn option does not appear while the native resolution is selected.. After selecting that option, I changed the resolution back to 1920x1080. The option disappeared again but as written in the link above, that width-height scaling option seems to continue working. Yis!
Thanks to everyone for their valuable input and the final solution for my friend Vordenator above.