I recently acquired 3 Lecroy broken scopes (WR6100, WR6050, WP7000), I took my chance to "waste" ~500$ for the 3 but did not regret at all in the end.
First I fixed the WR6100 few weeks ago with a similar symptom.
With the main plugged you could hear a tic tic tic ... all the time and the problem was on the PSU.
Luckily I was able to find the schematics for the PSU but I don't believe it is the same as the WR7100 one.
The fault was on the primary, after the bridge rectifier, a switching transistor was not able to create the 15V needed due to 2 dry electrolytic capacitors with high ESR and 1 dead diode.
A 2$ fix.
The WR6050 was not starting the DSO application.
After a quick check I found out that the Intel motherboard was having 3x 3300uF/6.3V very dry and opening up at the top.
Another easy fix, with 3 new caps it started immediately and works perfectly like the WR6100.
The WP7000 was supposed to be broken, but it already start to show some good sign of life.
I will open it up and clean it so if I can help with the PSU let me know as it should be similar to your 7100.
Those scopes seems robust and when a fault happens, not too difficult to fix.
Considering the price I paid for the 3, I am quite happy with the deal !