Sounds like it. If this an unmodified OG Gameboy, I have an original screen kicking around, if you want it. Really though, you should buy one of the new screen kits out there. I can personally recommend the OSD kit.
Everything you said - those old screens are finnicky at this point. Another recommendation for the OSD screen - game changer
Out of the 3 that I have, 1 unit is set for the FP IPS screen, 1 was going to be backlit with one color, and I have the first one I did with the yellow backlight.
I get that the newer kits are better - im not against them. I like the look of a backlit LCD a bit better, and installation is super-easy. I can use the screen half as a parts board