Someone has gotten the alleged firmware from LG, but turns out just to be the cross-compile toolchain and ucLinux. Well, anyway we know know that the BD370 and BD390 are based on that.
I don't think that there isn't a way to get console access to this device. A detailed network scan revealed this:
PORT STATE SERVICE VERSION
111/tcp open rpcbind
9736/tcp open unknown
44394/tcp open unknown
Port 44394 TCP returns a "500 internal server error", but probably just due to an incorrect URL. At least this means a webserver is running, so there is hope. ;-)