Thank you. This has finally worked for me!

Using Windows 7, NVidia (Geforce).

Excolion's solution helped a lot, and it was almost perfect, but not quite. Although it was generally quite smooth, at times there would be a lag, most noticeably when heroes move.

And I've tried a s***load of other solutions from the net with varying degrees of usefulness (setting desktop to 16 bit, compatibility mode, mouse polling and whatnot).

DXWnd finally is the perfect solution for me.

I can't tell you how happy I am after a day of searching. Not excited that I have to use 3rd party software, but it's much better than having to put up with lags or lower resolutions.

ZFRI: Tried your solution and it works a charm. I was having horrible lag on the adventure map and DXWnd has made it butter smooth thanks!

thank you all for previous investigations of this. I observed the same slowdown during battles, especially with 7v7 stacks. the discussion was helpful, but the solutions did not apply in my case since I run this on a Mac.

anyways, leaving this here for anybody running GOG HoMM IV on PlayonMac: I solved the problem by switching the Direct Draw Renderer from OpenGSL to GDI (see URL at bugs.winehq.org/show_bug.cgi?id=29287)

PlayOnMac Configuration -> HoMM4 -> Display -> Direct Draw Renderer (set to "gdi")

for what it's worth, I also set the video memory size to match my monitor (2048 Mb in my case)

runs in full screen 1248 x 1024 with no slowdown during battles

hope this helps!

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.

Gog version of Homm 4 Complete simply will not launch using DxWND. Nothing happens.

DXWnd turned out to be a poor solution - helped a bit for 5-10 minutes, after that the game got slow again.
I play GOGs HOMM4Complete in windowed mode in WIn7 x64.

GL wrapper solves the problem perfectly (links lower):
h t t p : // heroescommunity.com/viewthread.php3?TID=45412
Just unpack DDRAW.dll to HOMM4 directory and start game as usual.

Yes, DXWnd has been made obsolete by the wrappers

https://www.gog.com/forum/heroes_of_might_and_magic_series/graphic_gl_wrapper_for_all_heroes_heroes_of_might_and_magic_1_2_3_4_and_chronicles_for_better_wo

After all search that i have done on the internet i finally fix the lag proplem.It works perfectly and also on hd quality. I can explain if still anyone needs help out there. Wellcome back my childhood lets spend some quality time together.

You can explain ;)

Well, for him i guess (as he say some about HD) its about Disciples(4)GL wrapper mod.
As for original topic - 1280x1024 is 5:4 wrong proportions wrong resolution. Its 5:4 variant of 1024x768 for natively 4:3 video games.

And better avoid using this resolution even if you have 1280x1024 display. Such games where only 1280x1024 is maximum actual maximum is 1024x768.

For DisciplesGL set 800x600 and now choose resolution from GL wrapper setting.

I am trying to do some scripting and make a quest hut where you pay money to get increased movement for the day and tried to use INCREASE CURRENT MOVEMENT but it doesn't appear to work - I get the message that movement is increased with the horse picture but nothing happens and when you look at the hero the movement is steadily reduced every time I go into the quest hut. It was supposed to increase, so what gives? Is it buggy?

Might create your own post, but yes the movement script is bugged. If I remember correctly, +10 movement is the equivalent of adding 1 additional movement point to a hero. So basically you need to multiply by 10 for however much movement you want to add. The movement script cap is low, so you may have to have more than 1 movement script to get the desired result.

Edit. The movement script in Equilibris is fixed, so adding 1 movement instead of 10 is the way to do it in Equilibris.