Well, don't worry, it could be other things as well.
Have you tried static linking let's save that for later...
Are you sure there aren't any incompatible dlls in your %PATH%?
Try moving your exe and assets and new dlls to a separate folder. Then open a cmd.exe window and cd to that folder. Now type cmd.exe again. In the new environment (which inherits everything else) type 'set path=' and hit enter. Now try to run your program from within that shell and see what happens. You can type exit at any time to return to your original environment. This is to test what happens when the %PATH% is empty. It means it should look in the current folder only.
Next, have you made sure your current working directory is set correctly? It gets set to the directory you run the program from, which means, it isn't necessarily the same one. See https://www.allegro.cc/forums/thread/617730/1041133#target for details.
After that has been tried we can discuss static linking, to rule out bad linking.