Lack of a ground makes your equipment much more susceptible to lightning and other static discharge.
Of course, there's no way to prove that's what happened to yours, but before you replace it, I suggest you upgrade the outlet. If you can't do that (maybe you're renting?) then at least use a surge protector.

A surge protector won't do you any good if you don't have a ground. Unless you were hit by lightning or a severe power surge the missing ground is not the cause of your burnt out monitor.

If your CPU is plugged into the same circuit it, too, would most likely be zapped by a spike or surge.

And it might not be electrical at all. PC monitors are like TVs -- they occasionally just drop dead.

Thanks for enlightment.