Electronic – Low power, seven segment display

My first assumption from the symptom is that you have a single cathode resistor, which would explain everything. However, you say this is not the case and that you have individual 100 Ω resistors on each anode line.

The answer then must be that whatever is driving the cathode can't handle the combined current. Apparently you are driving the cathode with just a microcontroller output, which has insufficient current sink capability. Do the math. You want 10 mA thru each of 7 segments. That means whatever is holding the cathodes low has to be able to handle 70 mA. A microcontroller pin is very very unlikely to do that. See the datasheet.

The solution is to add a transistor that can sink the current from each of the cathode connections:

70 mA is easy for any discrete transistor you will be able to get. Let's say the transistor has a minimum guaranteed gain of 50. That means the base current needs to be 70mA / 50 = 1.4 mA. Figure the B-E junction drops 700 mV. With 3.3 V drive from the micro, that leaves 3.3 V - 700 mV = 2.6 V accross the base resistor. 2.6 V / 1.4 mA = 1.9 kΩ, which is the absolute maximum allowed base resistor. Given that, I'd use 1 kΩ between the digital output and the base.

Note that this will invert the common cathode logic from what you had. The microcontroller output now has to go high to enable a digit.

LCD display with a tritium backlight (half-life ~12 years) should be possible. The tritium emits beta particles that can excite phosphors to emit visible light. Glass is typically used to contain the tritium gas.

Watches have been made incorporating this principle, some Ball watches currently use tritium capsules for analog dial illumination, and there is at least one company claiming to offer micro-capsules.

Don't expect spectacular brightness, even nuclear-powered illumination has its limits.