My top screen is black after I found my Dsi xl on floor

If both hinges are broken, then there may be damage to the ribbon cable that connects to the top screen. You may have gotten lucky and the connection to the top screen came loose. Either way, you would need to be able to open the DSi and either replace the hinges (buy a completely new shell and top screen) or reconnect the ribbon cable to the mother board. Even if it is a loose cable, the broken hinges should be replaced to protect the ribbon cable from further damage.