What is a Church?

Opening a dictionary, you will read that a church is "a building for public Christian worship; the part of the whole Christian body." Is that what a church is? While growing up, I was taught by many men I respect and also in college that a church is a "a local, visible called out assembly of baptized believers." Is that a church? Can you use that definition and practice open/close communion? The catholics believe that a church is "all who, from the beginning of the world, have believed in the one true God, and have been made His children." (http://www.newadvent.org/cathen/03744a.htm) Now one can believe that definition and practice open/close communion. The very word 'catholic' means universal, in reference to its belief in a universal church. Then we open a phone book and look under "church." Here in our tiny Goshen, Ohio phone book, I find "Bridge Community Church, The Oasis Church, Knox Presbyterian, Whitewater Christian Church, Goshen Assembly of God, Abundant Life Fellowship, Grace Ministries, Adam Tracey, KingsWay, Adath Israel Congregation, All Saints Catholic, Agape Church, Cozaddale Baptist Temple..." Are they all churches? How can things so different be the same? Doesn't Eph. 4:5 read that their is

One Lord, one faith, one baptism.

So, they all can't be churches right? So that begs us to answer, which one is a church? Are the others frauds, organizations, clubs, or worse?
The very first time we read the word church in our Bibles is in Matthew 16:16-19,

And Simon Peter answered and said, Thou art the Christ, the Son of the living God. And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.
And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.
And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.

We see here a few lessons about the church:
1. The church is built by Christ. This is one of the most important works He is presently doing.
2. The church is built upon Christ. Not on Peter (see 1 Cor. 3:11, 10:4, Eph. 2:20), but upon the fact that Jesus is the Son of the living God.
3. The church did not exist until Christ came. The Lord started the church when He "called out" his disciples (Matt. 10:1-5) and commissioned them. The church could not have begun at Pentecost because that day there were "added unto" the church, the church had already been given its commission, instructions for discipline, etc.
4. The church belongs to Christ. He is the head of the church, not a man. He is the law giver, legislator, and leader of the church.
5. The church will be preserved through all generations. Since the time of Christ, there has been the church and will continue to be a church.
6. The church has been given the promise of Authority by Christ.
7. The church is not to be on the defensive, but on the offensive. We read that the gates of Hell cannot prevail against the church. Gates are used for defense, not offense. Too many times, we as members of churches feel like it is our destiny to be persecuted and beaten down, but 'Praise God, in the end Hell can't prevail against us.' Problem is, that is false teaching. We as members of our churches are to go out and take the Gospel to a lost world, knowing that there is no power that can defeat or hold back the power of that Gospel!
So, what is a church? Is the Yellow Spruce Community Assembly of the Church of God with Latter Day Saints Adventist Ministries a church?
Let us solve this, by looking at the Bible!