For example, the backlight is driven by T500 and/or T900, which have 4 neighboring caps, of which two are 100uf parts that leak profoundly. There are also a few more related to the chopper that drives it.

It is possible that the backlight tube is burned out or a transformer has failed, but there's no point in troubleshooting until the caps are ruled out. They are a 100% failure point and should be replaced wholesale.