Look in your newly created .skin file (should be named "Default.skin") and look for a SkinID property, if it has one, then you need to apply that SkinID to your webpart as well. If you want it to be applied to all controls no matter what, remove the SkinID property.
Also it could be that you're trying to reference a standard asp.net control
<asp:Button> and you need to reference the Kentico version
<cms:LocalizedButton> in your skin file. Make sure the control is the same. You should not have to recompile or do anything else, it should pick up automatically.