3 beeps looks like it's a RAM issue. Try popping out all the sticks and see what happens, it should do something if it works. If that goes then pop out different RAM modules and see if it boots, you may have fried a stick.
It may not display anything because there simply isn't anything to display. Just for kicks make sure that you have the TV on the right HDMI, and there should be a function button on the laptop that allows you to switch to projector mode or use an external screen as the default viewing screen.
Hope something works out for you!!! I've been there, spilling an entire nalgene bottle of grape juice on my macbook
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