I would like to take my heros game file or just the hero himself (personal stats and equipment) if that's the only possible solution, from one computer where I play, to another computer where I play. I want him off my laptop (which will not let me play the game), and to put him on my desktop without losing the whole game.

Is this possible??

I haven't really tried this with the GOG version but it should be easy. Heros are stored in a file called herodata.xcr so in theory all you need to do is copy that onto your other computer. In the first one I always grabbed the saved games folder, the hero data folder, (this does not contain herodata.xcr which is what you really need) campaign data.xcr and campaign heroes.xcr. Also grab the preselected hero text file and campaign hero text file. There's a fair chance you won't need all of these but that's what I always did just to be sure. All of these should be in the same directory as the game so it should be easy to find. Maybe grab the scenario folder if you have any custom maps you want to keep. This is for Warlords Battlecry one.

The other two should be pretty much the same but some of the data is in different spots. I think the files you want will either be in the specific games directory (Warlords Battlecry II for instance) or in the documents directory on your system partition check both and see if you can find all of the files you want to copy over. I don't remember if you can get the campaign data in the second or third It's possible it's in hero data if it's not there, I just don't know anymore. If you're having trouble finding anything just tell your machine to do a search.

I would recommend keeping all of the files intact on your first computer until you're satisfied with how it functions on your other computer just to mitigate the risk of losing something. I would note that I haven't done this personally with the second game and I haven't done this with the third in a long time so YMMV but you shouldn't lose anything except a little time if you're careful.