My laptop charger began to melt so I bought a new one, laptop was dead and now it won't turn on (plugged in)?

I think you should just take it to wherever you bought the laptop or an authorised hp bank. they will check it out and will probably find out what's wrong with your laptop. I think that the melted plastic will have some effect because it might have melted into the computer or it's blocking thing wherever the power needs to go. good luck. (: