MacBook doesn’t power on unless the smc is bypassed

Yes, you need both!

Here’s the battery MacBook Pro 15" Unibody (Mid 2009-Mid 2010) Battery and here’s the guide MacBook Pro 15" Unibody Mid 2010のバッテリーの交換

As far as the charger 80% of the chargers sold online are knockoffs! These are not safe and can damage your system!

A company I was supporting years ago had a 4 million bill for one of these! An employee forgot his charger, so he found a small computer shop which he bought it, Went back to the hotel he was staying plugged in his laptop so it was ready for the morning meeting with the client. Went to dinner and when he got back to the hotel, the place was surrounded by fire apparatus! He finally made it to the front desk to find out where the fire was. Of course it was his room!! They did give him a room for the night with just the cloths he was wearing. In the morning he had to vacate as all of the rooms where spoken for minus the floor is room was on.

It was a very expensive Charger! I strongly recommend going online to Apples web site to find the needed charger.