Worship in its simplest definition is the glorification of God by His children. It's not just the music. It's the preaching, the offering, the prayer, and the fellowship. If we are trying to get something out of worship for ourselves, like the "warm fuzzies" or an "experience with God" we're there for the wrong reason. Worship is for God and God alone. It's great if you get those feelings, but it's not like I'm going to listen to the sermon and make some deep theological connection that makes me feel like I'm on the edge of understanding God's purpose for everything.
We worship God by song, sure. And various people have various opinions about how song should be conducted and how it should be implemented. Some people want to sing 1600s Gregorian chants. Some people want to wave their hands and clap to the latest Christian rock. I personally prefer hymns. I believe God gets worship out of all of it if it's done correctly. However, any style of song can become less about God and more about man if implemented incorrectly. I often don't like contemporary Christian music's similarity to secular music, but it's just as bad to sing 50 verses of Just as I Am and not mean it, or to make it about the choir or the praise band, what have you. It must remain focused on God.
We worship with giving our tithes to God. I saw a CNN article recently that said most religious leaders don't believe the Bible specifies we must give to God. Certainly not! It is a commandment to give to the church and missions and the poor. Done in God's name, it is worship to God. Glad giving is one of the pinnacles of worship. Recall the poor woman's two pennies?
We worship listening to the sermon. We learn from God's word, and hearing it taught and expounded. If everyone falls asleep, then it's not very good worship, is it? You may not be moved by the Spirit (though you certainly can be!) but learning and growing as a Christian glorifies God.
We worship through prayer--I'd wager prayer is one of the most important ways, because instead of singing lyrics someone else wrote, we say what we want to say to God. Again, it must be done properly. Reciting chants or prayers and doing it emptily is likely not worship--it's just a person saying something. Praying to God by pouring out your heart, whether it's emotional or not, is worshiping God. We praise, thank and intercede during prayer. It's commanded of us.
Worship of God extends beyond Sunday morning. It even extends beyond Sunday night and Wednesday night. We worship God during our daily devotional. We worship God in our own prayers. We worship God by being a light in the world in our daily lives. All of this is worshiping God.
To answer your other question, you have to like and want to do what you're doing to worship God. If you hate the music, you're going to tune it out, not sing it, or just go through the motions. You're not worshiping God. That's why you need a church that worships with you. If you can't stand the pastor, you aren't going to be edified. It's important to be in a body of believers that worships in a way you can worship God and not be distracted or bored. It's not a sin to like a style of worship, be it music, sermon, or Sunday school, over another.
