Best (and only way) is to provide power to the rails the Wii requires to boot up (those being 3.3, 1.15, and 1v - assuming you didn't remove the LDO for 1.8v stepdown). You can easily confirm the trim is booting without hooking up any USB drive as well. You will get a black "no USB" screen that will confirm your trim is working as intended. Hook up composite video to a screen to confirm video output. If there is no video signal present on your display, double check your wiring. TL;DR - wire up composite video, provide a voltage to each of the Wii's power rails and ensure common GND between everything. Turn on regulators and make sure you're getting a video signal.
Before you do all of this though, make sure you check the resistances of all voltage rails to GND for shorts. The 1.15v and 1V rail are very low resistance to GND (around 40 and 70ohm iirc, I might be wrong there though). Please upload some pictures of your trim as well, it's impossible to diagnose any issues if all we have is text! It's hard to kill a Wii unless you doing something stupid, like slicing NAND traces or cutting vital traces. Just follow the Trimming Guide and you will be fine.