With the phone on, use a torch and shine it at an angle close to the screen to discern if the home screen is visible. If it is there at all it will most probably be very faint and hard to detect.
If you can detect the home screen display, then you have a backlight problem. The problem could then be either in the systemboard backlight power supply, the cable connecting the screen to the systemboard or in the screen itself.
If you cannot detect the home screen display, The problem could then be either in the systemboard, the cable connecting the screen to the systemboard or in the screen itself.
Apologies for the vague answer as in either case the phone would have to be opened and the fault further diagnosed as to what is actually the cause and what parts if any need to be replaced.
If you cannot detect the screen or even if you can and you wish to take a gamble, here is a link to a list of suppliers of a LCD screen for the phone. It is not a recommendation to use any of them , it is just shown to give an idea of the price. There are others online that may suit you better. Just search for Nokia 6555 LCD screen replacement part.
Here is a link to the Ifixit repair guide for a similar model phone which may be of some help towards replacing the screen.
Nokia 6555b Logic Board Replacement.
Hopefully this is of some help.