Why does the furnace turn off when the thermostat’s LCD dims

heating

Recently I replaced an old mercury thermostat with a programmable digital model (a PRO1 T955W).

It is set to operate in Heating mode. The desired temperature is set to 70 and the in-home temperature is in the low 60s. Yet, the oil-burning furnace does not turn on.
As soon as I touch the LCD screen, its back-light turns on and shortly afterwards the furnace motor starts running/burning. Then after a few seconds, the LCD dims, and the furnace stops before the desired temperature was reached.

I was initially wondering if I might have switched around the R and C connectors. The thermostat only has those two inputs. After switching them again, the same problem persists.

Any ideas?

EDIT:

Here is a picture of the wiring. It shows the R & C wires. The insulation looks a bit worn. I have made sure that both cables are securely screwed into place.
Picture of Wiring

Here is a picture of the back side of the thermostat:
Picture of backside

Here is a picture of the thermostat display when connected. Here the display is lit (after I pressed the display), and the furnace immediately turned on. As soon as the display dimmed (after a few seconds of not touching the display), the furnace stopped immediately.
Picture of thermostat display

Best Answer

What happens when you short out the two wires? A simple mercury thermostat does that to turn the furnace on, so when you do it the furnace should come on.

If that works, then I'd guess that the new thermostat is defective.