@ellasimones so it remains black no matter what (old or new screen)? The white light means that your LCD receives the backlight but no video signal. So you'll have to check the connector where the LCD plugs in and check for bend, broken, corroded pins etc.
The backlight and the video have separate circuits. For the video processing you would have to check the IC201 which is the signal processor on the on the SY-243 board.
Basically what you want to do for now is to disassemble your camera and check the board for anything odd (missing or burned) component.
You can always post some pictures of that board with your Question so we can assist you with that. Adding images to an existing question
Also, you can now download the Level 2 and Level 3 SM from the bottom of this page Sony Cyber-shot DSC-W330. It'll help you with finding the components as well as trying to fix it.
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Just tested my old LCD and it doesn't turn on at all. I'm guessing I messed something up >:(
crwdns2934271:0crwdnd2934271:0 ellasimones crwdne2934271:0
@ellasimones not necessarily. Try you new screen again and see if it still shows white.
crwdns2934271:0crwdnd2934271:0 oldturkey03 crwdne2934271:0
@oldturkey03 tried it as well and same thing :(
crwdns2934271:0crwdnd2934271:0 ellasimones crwdne2934271:0