Second client has to be connected while game is playing. It looks like some software blocks thing from playing. PokemonOnline.exe should have rights to connect as well as tibia client does in order to game work. If it shows "Game hang due to lag" window and never dissapears, it looks like connection is still present (otherwise, window would be hidden - if 2nd client is not connected then window is not shown, because on loginscreen you would have "hang due lag" window show anytime).
Its kinda hard to address your problem because its only u who have that kind of problems. The connection of other players remain active until they logout or become kicked from game, but under normal conditions, the problem with neverending "hang" thing and poke windows not showing does not appear.
First of all:
1. Check if software/hardware does not block a connection to server. So follows all routers, all firewalls, all antivir things, "windows firewall" thing etc. Connection must be cleaned for PokemonOnline.exe.
2. If still this doesnt want to work correctly, check if you are really using latest updated client. Try to delete version.xml file from ./data/ dir and let updater to download things again.
If it still does not want to work, create file in ./data/ dir named "debug.txt" and run client again. You will see a strange window, minimize it and wait till client will disconnect, and then bring window back and copy everything is pasted there.
Too bad I don't have money for a 64 arch machina and Windows 7 so I cannot check it by myself.