What will happen if I drill small holes in a flatscreen monitor?

A fucking gnat crawling on my screen turned out to be a fucking gnat crawling in my screen. Obviously I must now drill into my monitor to remove the corpse after squishing and realizing this (to my great horror).

In reality, I have no idea what to do. DIY take this apart? Wait for it to dry, rot, and fall down? Buy a new monitor? Sigh.