Well, I doubt it will have anything to do with your hardware such as routers, et. al. It only occurred when you switched to the latest version. The first thing to think about is do you need the newest version? I am using 4.06.
Kevin is correct about the speed test. It may help. Do troubleshooting which always involves isolating things and doing one thing at a time. For instance, log off all computers but one and see the speed. Also, write down everything you see when it is opening such as loading patients, etc. They all go rather fast for me. Try to pay attention to see if any one thing is slowing it down. Say, that the point where it is checking interfaces takes 30 seconds, then you have possibly found the problem.
This also begs the question, "how often do you log in?" I haven't logged out of my AC programs in my rooms in over a week. Not good, because I should be logging off the computer, but I always forget. The staff has to log on in the morning or if they change computers but that is rare. So, for me, five seconds vs 90 seconds wouldn't make a difference, although it would irritate me on the times I had to log in.
*****ALSO: Are you completely shutting down AC when you "log out" or just logging out. The slow part is opening AC when it is completely closed as you have to open the application and authenticate to the server and load everything. But, if you just need to log out so another user can log in or you want to keep the data secure, then just hit CTRL - N. At the login screen at that point, it only takes me about one second to log back in. If you are a mouse person, then just click on File and Logout.