I've taken it apart (in Dave Jones speak), found no issues, re-assembled and now the meter powers up.
I'm no expert, but I'm learning about how DMMs work and I can offer suggestions.
Can you post clear focused photos of your pcb (front and back)?
Symptoms:
1. DC mode: 0.0000v indicated and does not move with input; 10.50 Megohm shown in secondary display and does not change when shorting leads
2. AC mode: 000.00 mv indicated and does not move with input; 1 Gigohm shown in secondary display and does not change when shorting leads
3. Ohms mode: 00.00 Ohms indicated; 2.5V shown on secondary display (1/2 of 5V vcc?); LCD display dims slightly when shorting leads with no other change shown
4. Capacitance mode: main display shows no digits and is constantly toggling between uF and nF; 2.5V shown on secondary display (1/2 of 5V vcc?); LCD display does not dim when shorting leads as it did in Ohms mode
5. Hz mode: display moves about in a range around 30Hz with 000.00 V on secondary display. The LCD display dims slightly every second, and just before the Hz display is updated. Holding the POSitive lead causes the display to read around 120Hz
6. Diode mode: 00.000 V indicated; 1ma on secondary display; Shorting leads dims LCD display slightly;
7. Microamp mode: 0000.0 uA indicated; 100 ohms on secondary display; Shorting leads has no effect
8: Milliamp mode: 0000.0 uA indicated; 100 ohms on secondary display; Shorting leads has no effect
9: Amp mode: 00.000 A indicated; 0.01 Ohms on secondary display; Shorting leads has no effect
For 1, 2, 7, 8 and 9, the primary and secondary interface are displaying correct, according to the manual, for no input. Obviously, it should show something other than 0.0000 with input for 1 and 2.
For 3 and 6, the primary display should show 0L, overload, with no probes attached.
From the above observations, it almost seems like something is shorted for 1, 2, 3 and 6 causing it to display 0 all the time.
The meter has a single A/D converter, a Cirrus Logic CS5508BSZ, which is a nice but expensive (around $20 usd) part.
I haven't seen this ADC before so I will have to do some reading/studying.
As a simple test, test VDC with 10V input. See if the network resistor input divider show the appropriate ratio drop.
In addition, you might want to measure the current draw of the multimeter. According to the manual, it should be 7mA for most modes. If the current draw is signficantly higher, then something is shorted.
PS. The battery life for a zinc carbon 9V is 36 hours according to the manual.