[Galaxy Tab 2 Q&A, Help & Troubleshooting] BoneWithABeagle:
Well, in this rather sad case it's almost safe to assume that there's a software issue between the software stack for the dock and the device encryption (though that's freakin' weird that Samsung's QC didn't test out this particular scenario).

Yeah. I understand that all sorts of wireless connectivity is a absolute no go around medical equipment, especially in ICU's.

However, that security model a bit through the roof. While I understand that patient records are confidential and the internal network of a hospital is a critical infrastructure because equipment could be interconnected, it's not that easy to hack into the system through a active BlueTooth connection (especially not when the default on Android is "Not visible") ... your WiFi network (by the end of the day your tablet needs to somehow connect to the LAN, and since the Tab 2 doesn't come with a ethernet jack that only leaves us with WiFi) is the more vulnerable attack vector for someone really wanting to get in (for whatever ill intent). However, we don't want to start a "network security" debate here.

There are two ways to get to the system log. One way, enabling you to catch the boot-up process, is to turn on adb debugging in the developer options on the tablet, have the tablet connected via the charging cable to a PC, have the drivers and "adb" installed and "adb logcat > logcat.txt" running so it starts fetching the log at the earliest moment possible (as soon as adbd was started on the tablet).

The other way is to install, for example, "CatLog" from the Play Store. This program displays the logcat output inside a nice application right there on the tablet and also enables you to write the log-roll to a text file for further analysis. This doesn't get the early log output, but running it right after a boot-up and letting it record while you try to mess about with the dock's keyboard will get as much data as somehow possible in case it would show a error related to it (logcat has a bit of a buffer, when invoked fast enough it might be able to get to the bits of the early log).

One "security concern" involved here (in regards to the slightly paranoid setup of your work place(?)) is that this log contains a lot of data you may not want to show to the public - like the Google e-mail address associated with the device, several IDs like the one of the WiFi AP and the tablet and so on... you can even see which apps have been launched during boot. That gives away so much info to make a system/network admnistrator already wearing a tin-foil hat to totally go bananas.

Well, apart from the latent chance that a fix might be impossible, the main problem I see is that it's obviously a employer issued device (given you're from the nursing staff and not a patient of the facility) therefore hard to give out logs to strangers on the Internet for "look-see" when you're already trapped in a tin-foil hat wearers environment. To try and track down the problem one needs to see what's going on with the device, and that would mean laying eyes on data that's surely deemed "our admin eyes only" in your case. That, at least, would be my definition of the "main reason for the lost cause".

Anyway, if you can install CatLog and review the log and spot a meaningful error feel free to post the bits relating to just the error instead of a full system-log.