I recently bought one of these units and ran into this exact problem.
The service manual was quite easy to find on the net and I noticed that the LCD seemed to be Hitachi HD44780 compatible. So, I bought a standard LCD 2x16 characters and hooked up but it did not work, the same blank display.
Information on the internet is quite sparse about this problem, but I found a post in Spanish which I figured out indicated a problem with the contrast voltage, see schematics below. After changing the termistor/resistor voltage divider to a 2k trimpot, see image below, the leftmost marked rectangle, the hooked up display worked like a charm. This proved that the electronics controlling the main parts of the electronic circuitry worked. Changing back to the original display, it did not work, so I realized that there must be another problem. Also, there was no way to fit the hooked up standard display with its larger footprint into the crammed space of the unit. Back to the drawing board to try to solve the problem with the original display.
Another post about this problem, buried within a review on Harmony Central indicated that there might also be a problem with the capacitors connected to the LCD controller. I had noticed these capacitors, and thought that they might be the problem. Electrolytes have a tendency to fail over time and when I removed and checked them, there are three of them, all seemed to have failed. The value of these capacitors is 4u7 16V and I replaced them with compatible Tantalum capacitors. See image, the rightmost rectangle. I fired up the unit and the display worked again!
To solve this problem, first try to change the resistor/thermistor voltage divider. The only thing needed is to lift the lid of the unit. If this does not work, change the capacitors, which need much more disassembly of the unit, mainly including removal of a metal plate that covers the front panel from behind.
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