Hi @jazzier ,
I couldn't find a service manual for your model so perhaps the following may be of some help but maybe not. Hopefully it will be so it may be worth a look in your receiver.
My reading of the Caution notice on p.4 of the Marantz TA 170 AV Service Manual seems to indicate that it is very similar to the TA110 but obviously some things have changed. In the parts list for some parts, it specifies what the part number was for a TA-110 and now for a TA-170. The display module has only the one part number listed, so based on this I was hoping that the display module would be the same one used in both models and therefore the backlighting would be powered the same way.
It is a FIP7P8C (Marantz part # HQ30705060) which uses a fluorescent tube for backlighting. The link is all I could find in the way of spare parts by searching for the part type and also the Marantz spare part number. You may have better luck.
The fluorescent tube (presumably not separately removable from the module?) is powered by a 2.1V AC supply directly from a secondary winding of one of the power transformers.
Perhaps check if there is this voltage being supplied to the display module on pins 1 & 26 or on the appropriate transformer connections.
Here's a composite image from the schematic which may help.
(click on image to enlarge)
If the transformer winding is faulty, I couldn't find a replacement transformer either.