studio 1537 lcd replacement

hey everyone, I need some help with ordering new parts.

my sisters laptop broke, the lcd screen went white. We concluded it was the lcd because the cable was not loose and the motherboard was fine (plugged the laptop to an external monitor and worked fine).  Anyway, i ordered a replacement screen for it, and it was not the right screen. so now i am confused, i know the laptop is a studio 1537. I dont know what the part number is for the lcd i need to get.  

i found b154ew09 on the back.  but that looks like it is the same part i ordered.  if someone knows if that is the right part or not that would help me a lot

next question:

when i order the new lcd, do i need to get a new converter as well?   the reason i ask is because the one that is currently attached to her (broken) lcd is attached with a flimsy cable strip (whatever the technical name is).   The first lcd that i ordered had a plug for the inverter, while the current inverter we have has no place for a plug.    

i tried to spell that out as best as i could.  if there is anything else you need, i can try and find the answer.

thanks everyone i appreciate it!!