StonyYodelers basically said what you need to know, but I'll re-iterate and expand on some stuff.
There is a "white screen" section here. Please make sure you've looked at everything there, first.
https://www.freeplaytech.com/troubleshooting
One thing that CAN happen is that the SD card can get corrupted if the initial bootup doesn't properly happen. Here's a rundown of how it works.
After you burn the SD image to the SD card and boot it up for the FIRST time, the operating system will resize itself to fill the entire SD card (because people use different size SD cards). When it's done, the machine should shut itself off. Sometimes this is quite alarming for people that aren't expecting their system to turn itself off, but it's normal and should only happen once.
After that, all subsequent bootups should work normally.
Press and hold the power button. The screen turns white.
Hold the power button until the green light turns on.
Let go of the power button.
The screen goes black and the system shows RetroPie and all that.
BUT, if that FIRST bootup (that shuts itself down automatically when it's done resizing) gets interrupted, the SD card may become corrupt. Then, basically, nothing will work correctly, and you have to start over. Who knows what the system is doing, then, unless you connect to HDMI (like Stony mentioned).
So, if you want to inspect things further, connect the system to a TV/Monitor via HDMI. Otherwise, I'd check all the stuff that StonyYodelers mentioned and all the stuff in that troubleshooting link. Then, I'd start over with burning the SD card image to the SD card.
But, anyway, if the green LED is coming on after you hold the power button for a few seconds, then that's a good sign that the operating system is booting up. Then we just need to figure out why there isn't info getting from the Pi to the LCD.
Oh, also, you can detach/reattach the Pi itself. There has been a couple rare instances where that's fixed random connection issues like this.
https://www.youtube.com/watch?v=Hn_pFBwEQxA