I can answer some of these questions, but once again, not enough information is providerd. (I don't mean once again aimed at you). But, it is much easier to explain or troubleshoot if the given issue contains the hardware and software.
The biggest piece of information is what version or type of SQL Server you are using. Right off the bat SQL Express can only use 1GB of RAM. I am assuming you mean 4GBs of RAM. Using the IP address is many times preferred if it works for connectivity. This puts DNS out of the picture. If something occurs, and AC tries to find the database again, and DNS can no longer resolve the IP, then it will not connect. On the other hand Computer ExamRoom1 will likely always be ExamRoom1, but the IP especially if you are using DHCP may change after it requires a new lease. Even then, it usually gets the same IP, but not always. Please let me know the type of SQL Server you are using.
Also, on the server or main computer, please give how much RAM it contains.
