Solved the no power up issue. When the button is pressed, there is no display and Step-up/Boost IC at U5 is so hot. It could burn your finger. The fault is the Schottky barrier diode at D2. The diode with marking code SS18 (1A, 80V) was tested fine both in-circuit and out-of-circuit. Replaced it with SR2100 (2A, 100V) and the unit is working again. Measured the peak voltage of 52V at the cathode side of SR2100 Schottky diode when the button is pressed. Since the voltage rating of 1206 SMD capacitor at C11 is only 50V. Eventually C11 will give up. I replaced it with an electrolytic capacitor Rubycon 4.7uF @50v. I couldn't find a higher rated voltage of capacitor. Ideally should be like 100v. However, when I tested the Rubycon withstand voltage, it could go up to 100v. No wonder Rubycon capacitors are good. Anyway, fixed the unit by replaced two components at D2 and C11. See photo fixed.jpg.
From the transformer, when the button is pressed, there are two outputs, 9v (for powering the unit) and 37v(at least for Zener diode testing). See photo Bottom.jpg. Mine was like 2v on either path. Obviously there was a short somewhere. Through the process of elimination, I removed Schottky diode first. I got the 9V back. At first I thought ATMEGA324PA was the fault, but it was tested fine when applying 5V directly. See photo Top1.jpg and Top2.jpg. At first replaced D2 with SS24(2A, 40V) for testing. Obviously the voltage is not rated high enough. The diode was so hot and high pitch sound can be heard from the transformer when power up. Since I don't have any other SMD Schottky diode with a voltage rated that high. I used a through-hole Schottky diode SR2100 and there is enough space to install it. For the capacitor at C11, it will give up eventually if the peak voltage repeatedly go above the rated 50v 1206 SMD capacitor. This maybe the reason why people reported C11 shorted in the forum.
My LCR-TC1 is from the original creator. The original has 3 Chinese characters (浩祺心) on the top of the circuit board. See photo Top1.jpg. The component layout may be slightly different than yours since there are so many clones out there. However, the general layout is the same.
I have been troubleshooting this unit for a while. Replaced numerous Step-up/Boost IC ALxxx at U5 with different numbers. xxx are three numbers. The numbers do not matter if anyone who cares to know. Even bought STC15L104W chip at U4 and programmed it. By the way, I couldn't find the original U4 firmware. Luckily I didn't overwrite the original chip. Obviously none of them worked until I replaced Schottky diode at D2. The time and money spent may not justify, but the feeling of successfully fixed the unit is worth it. Hope this post will help someone out there.