I looked up the manual for your meter (
http://www.panda-bg.com/datasheet/646-3 ... MS8268.pdf) and it says that your meter has a 10 megaohm input impedance in the DC range, so you should be reading voltages closer to 200V than 100V. How does the voltage on TP1 vary as you adjust VR1?
From the voltages you gave me, it seems like Q3 isn't switching properly.
Try this:
Remove U1.
Then measure the voltage on pin 4 of the socket, it should be close to the battery voltage 3V. TP2 should also read around 3V.
Then take a small piece of wire (like a resistor lead) and short U1 socket pins 3 and 8 together. Then measure the voltage on pin 4 again. It should be less than 0.5V. The voltage on TP1 should be close to 0V.
This will tell us if Q3 and Q1 are working.