The dashboard instrument panel is electronic and all the power and sensors connect to it via some multiplugs on the back of it - usually two plugs.  There's a loose connection on one of them by the sound of things, either the main power feed to the panel or the earth.  Pull the plugs off (carefully), make sure none of the pins on the panel connectors look bent, then re-connect the plugs and make sure they're fully home and tight.  If you have some switch cleaner or electrical contact cleaner you could spray it carefully onto the plug contacts, but don't get it all over the place or you might find your fascia or seats dissolving!!  You don't say which BMW you have, so I can't tell you how the instrument panel comes out, but usually there are a couple of screws around the top of the inside of the dash coving.  Take them out and carefully prise the coving out - always be very gentle, stop if something's not moving and figure out where there might be another screw.  Once the coving is out, you'll see the screws that hold the instrument panel in.  Remove them and pull the panel forward to get to the plugs on the back.  The screws are often hidden or concealed, so go carefully, and make sure you've found them all.  Forcing things will usually break something!

Tim