MapWinGIS uses CAtlHttpClient for tile requests. I believe it uses default port 80 since they are HTTP requests. URL naturally depends on the provider. I'd suggest to examine the issue with Fiddler. MapWinGIS requests can be intercepted by Fiddler by setting:
Sergei
axMap1.Tiles.SetProxy("127.0.0.1", 8888); // where 8888 is the default port Fiddler uses
Hope this helps,Sergei