Just be sure which LCD screen you will order. A general search is not always enough. FIRST you have to remove the old screen, write down it's model which is located on the back (it's not a very long string of letters and numbers) and search by model No. so you can be sure you are ordering the correct part. Pay attention to the version too. Some lcd screen models have versions (e.g. v. 2 or v. 3)
Try to turn on your laptop without the battery on (only with the plug adaptor). If this doesn't work, it is probably a hardware issue (although more inspection is needed before reaching this conclusion).