The LCD screen is dark when I shoot, even when I am not in a dark environment. Sometimes it's also blurry.
The pictures come out fine when I use flash.
Is there a problem with my screen?
This is not a problem with the LCD screen. The images are under exposed.
In easy terms, not enough light is hitting the sensor to 'take' the picture, so it's coming out black.
When it's blurred, it's because the shutter speed is too long and is recording everything in sees in the period of time the shutter is open (hence the blur as if you're handholding, you will be moving the camera).
It works when you fire the flash, because that's illuminating everything you see.
I suggest learning about the exposure triangle.
I notice in the picture above you're in a darkened room as well. One thing to note, it may appear light to your eye, but your eye is considerably more senstive to light than your camera.
In addition to the above answer, theres a super bright bit in that image beyond the camera. It has to do maths (metering) to work out the exposure for you when you are in auto/P mode. If you are metering using a bright window it will assume the whole image is this bright and your dark areas will end up underexposed.