Does your LCD TV have regular RCA inputs? Try plugging the green plug into the yellow socket and view on AV, you should get a black-and-white picture in interlaced mode (480i) and no picture in progressive mode (480p). Please note that if you change into progressive mode you'll need a progressive TV to change back into interlaced, so for now just check that you get a B&W picture on AV. If you have success with this, then maybe you have the wrong source selected when connecting to the component inputs? The source may be called YPbPr instead of "AV" or "Component". I have a TV like that, seems kinda funny since most people wouldn't know that YPbPr = component! If it still doesn't work, try connecting your DVD/Bluray player to the same component inputs that you were using for your Wii and see if there's a picture. If there's no picture, then it could be that the inputs on the TV itself are bad. Also bare in mind you cannot unplug the Wii's cable and plug it back it in again while it's on, this itself results in no picture. You have to switch the Wii on with the cable inserted in the Wii or you'll get no picture.
Hope this helps.