Seems almost like you have a firewall that is preventing the first connections from happening and then it goes to alternate ports or you don't have enough memory.
I use my old Vista gaming machine to play - it has 12 GB of memory.
I can run 4 clients simultaneously and can log 2 in together in less than a minute.
I just have the memory leak issue where, where a client approaches 2 GB, it takes forever to switch characters, zone, buff (where it changes UMD) - even when only running 1 client.