So suddenly it is TWO people out and one person in, and the hardware has been shuffled? And one of the two people who are out DIDN'T get new hardware?
Now it is imperative to get your people to carefully note the time on their system clocks as to when these crashes occur, so that you can look in the system logs (that is "generic system" as opposed to only the SYSTEM logs by that name). If you have a desktop clock gadget, that would work as a time source. The date/time info in the lower right at the end of the task bar is accurate enough because unless you have a hardware cascade failure, there will only be one or two logs in a given minute on a normal machine.
Something else to check. If the person IN the database gets out, does the .LDB file go away? And once that person is out, can you suddenly get IN? Or can that other person get in? This could be any of several issues having to do with permissions. We need more data about what works across your set of users.