i searched ebay a little bit and found a battery cover/holder.
i don't know whats normally in the leapster l-max - but this holder looks like a 4 x aa battery holder: [http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=370414876030&ru=http%3A%2F%2Fshop.ebay.com%3A80%2F%3F_from%3DR40%26_trksid%3Dp3907.m570.l1313%26_nkw%3D370414876030%26_sacat%3DSee-All-Categories%26_fvi%3D1&_rdc=1|CLICK]