1. while unleashx is on your screen, press the Y button on the gamepad. the system info window will appear. scroll down to almost the very bottom. the unleashx version is on one of those lines.
2. from what you described, your xbox is indeed soft-modded. the soft-mod was installed using the 'hotswap' method of connecting your xbox hard-disk drive (hdd) to your PC. if your xbox boots directly into unleashx or any other app besides the ms dashboard, then your ms dashboard executable has been renamed. it's original name was xboxdash.xbe. now some other executable is using that name and you must determine what the current name of the ms dashboard is. it is most likely something like 'msxboxdash.xbe' or 'xb0xdash.xbe' or something similar. if you want to use the ms dash to play dvds and you want to be able to do it from the 'Launch DVD' item in your unleashx menu, you must configure unleashx to launch the 'true' ms dashboard instead of xboxdash.xbe. you do this configuring in the 'Autolaunch' section of the Control Panel (system, settings from the menu). in the Autolaunch section, you need to set 'DVD Player' to the new path/filename of the ms dashboard. save. exit. maybe even reboot. after that, if you have set the path/filename to the correct xbe, you will be able to 'Launch DVD' from your UX menu and the dvd will play.
others have recommended using dvd2x as a dvd player. it is a fine dvd player also. if you choose to use that, the steps above apply as well. instead of pointing 'DVD Player' to the ms dashboard executable (xbe), you will need to point it to the path/filename of dvdx2.
the previously mentioned method for playing dvds from xbmc may or may not work depending on how xbmc is configured. for help with that, please go to the xbmc forum.
3. (how to tell if your bios is modified)
a lack of standard terminology makes this a little confusing. when you get a new xbox (that is not modded) you are running off what i call a MS/retail bios. if you mod your xbox to use some other bios, you are using what i'd like to call a 3rd party bios. if you edit a 3rd party bios, then you are using a modified 3rd party bios. obviously, you are using a 3rd party bios if you boot into anything other than the ms dashboard (like booting into unleashx). determining whether or not it is a modified 3rd party bios would take alot more typing and guess-work on both our parts. modified or not, it has no bearing on your ability to play dvds.