Situation: Wanted to check some LEDs on a repair project, grabbed my U1272A, switched it on and wanted to engage the backlight, because it helps me with clear reading. Nothing happened, only confirmation beep that the setup/light button was pressed. No error message. Setup worked fine, also reset to defaults worked.
What to do?
Battery on the LCD still read three stripes, so should be full. Measured the 4 AAA cells with a bench DMM, 1.45V open circuit voltage. So, not totally good, but on an acceptable level.
Dismantled the whole PCB, unscrewed everything, separated the LCD module from the PCB, which is very nicely realized in this DMM.
Measured with a Fluke 8600A bench DMM in diode mode the LEDs, got 1.77V, so theoretically it should be ok.
At that point I wondered if I should adapt some connectors to make the LEDs light up, or simply try fresh AAA cells first to rule out other complications.
Put in 4 fresh Varta Professional cells, and all of a sudden the backlight worked again.

Stupid moment, but maybe helpful as a reference for other people who encounter similar symptoms with their DMM...