When I try to insert a memory stick into my sony cyber-shot dsc-p20 it won't lock in place and I can't close the door. Help!

Your camera uses the regular sized memory stick.make sure your using the correct size.make sure that your inserting the ms the correct way.see:p.17 of your manual for reference.btw,are using a ms adaptor?if yes, try to make sure you insert the ms all the way in the adaptor so that no space on the actual ms is sticking out of the ms adaptor.it should be the same size with the regular sized memory stick. if not, insert the ms firmly until you hear a clicking sound.the ms should lock into place.if it doesn't then the spring lock of the ms compartment might be faulty.that unfortunately,would require repair. but i hope this info helps. thanks:)

Try quickly pushing the card in and letting it go, fast. Keep trying this and see if the card finally locks, you could have a build up of fluff on the latching mechanism. doing this could free the fluff and problem solved.
Its also possible that the latching mechanism has dislodged which means a dismantle at a repair shop.