My lenovo yoga 720 15IKB was working as usual. It was on lock screen when it went to sleep mode. since then it hasn't turned on.

the charging led doesnt glow on plugging in neither does the power button doesnt glow when pressed. its completely cold! 

please help me out!

First thing to do is check the charger. Try a different receptacle and/or a different charger. If a known-good charger doesn't work, then the issue is likely something that'll require servicing. 

Thanks, but I've tried using another charger but it didn't help. The led does not glow at all. There's still some charge in the battery so ideally it should boot up on its own power but it doesn't. 

I have also tried to disconnect the battery but the connector is glued so I didn't attempt to tamper it. 

If the NOVO button won't start it, then it's probably time to send it in. Probably time, anyway.

The heating has melted the bezel on the bottom left of the screen

I can't tell you without getting hands-on, but it sound like something's shorted. Anytime you have things melting, it's time to step away and get a service center to handle it. If it's still under warranty, perhaps you have a friend in the states who could handle that for you. Maybe someone else has a solution, but every time I've run into an overheating or shorting issue on a computer, it's toast. Literally.

Oh crap! That sounds bad. Guess Ill have to forget this machine for a while. Well, thanks for your help!