Do you have another AC adapter at hand? (Any adapter with an output voltage of 19V, a matching plug and correct polarity (negative on the sleeve of the plug) will do.) That will help you narrow it down to either the AC adapter or the laptop itself. (I’ve had power issues with laptops two times, and both times it was the AC adapter.) If it’s the AC adapter, replacements are easy to find—a lot of HP ones are compatible, and also some generic or third-party ones—see above for specs. If the problem persists regardless of the AC adapter and you have access to a port replicator, you could try that to narrow the issue down further. If the laptop runs on AC power when docked but not with the AC adapter plugged into the laptop, it may be due to a faulty power jack (or wiring).

First, not every 6930 has a WWAN adapter, and even those without have the SIM slot. If your 6930 came with a WWAN adapter, there is an extra sticker behind the battery, next to the main label, indicating the type of WWAN adapter installed and the IMEI number. If you have the WWAN adapter, the rest depends on the operating system. For most Windows versions, you either have received a driver CD; if not, look on the HP website for WWAN drivers. Under Linux, things get a bit hacky, as the un2400 adapter requires a binary firmware blob that you would need to extract from the Windows driver, as I’m not aware of any Linux distro shipping it. Unfortunately, in my own experience, I never got it to work under Linux.