It sounds like you somehow blew up your Arduino, but I don't see how that happened. There are no red flags in what you said you did. I'd say if blink doesn't work, it's dead.
Then about your experiment: such a transistor has a gain of about 100 (or even more), so to drive 5 mA through your LED (more than enough for modern LEDs to "shine brightly") you have to sink 50 µA of current into your body. That is quite reasonable for a normal sized human (your body has a significant capacitance, and the charge is leaked out through moisture in the air), so you're not doing anything wrong there: this is expected behaviour. Now you also learned one way of introducing noise into your circuits, as it works the other way around just the same: you are an antenna for the 50 Hz (or 60 Hz) mains field that's all around you!
I don't know why the IDE still thinks it's successfully uploading the sketch.