I'd suggest you not try fixing the phone yourself. The videos make replacing a screen look easy, but it's more difficult than it looks. If you do it right, on your first try, you'll be spending the better part of a day. Chances are, though, that you won't do it right and something else will go wrong. Or you'll replace the screen, but it's a cracked motherboard. Or you'll order a new screen, open the phone and find out that the only problem is that the screen cable plug came loose.
Call it and if it rings, that's a data point you can give the repair shop to make their job easier (which translates in less labor you have to pay for).
Mess the phone up when you're trying to fix it yourself and no reputable repair shop will touch it - the cost for analysis of the problem will be more than the price of a new phone (they're less than $90).
You may want to reconsider fixing it. A good used screen can run almost as much as the whole phone. If it's the motherboard, it can run $35-$50. It usually doesn't pay to repair phones that cost that little - the difference between repair-it-yourself price and replace price isn't that much. (A good repair shop would offer you a new phone for about what they'd charge you to replace the screen. Or just tell you to go to the carrier and buy a new one. Some shops are honest.)