I'll admit I didn't take the time to listen to the entire 1-hr. sermon. (Sorry.) But I can still answer your question. Your salvation is matter of status, and not of anything else. We get filled with anxiety because of life factors, circumstances, and our own regrets. Our emotions can churn, and our brains can spin with all kinds of thoughts. But salvation is a simple "legal" agreement between you and God that can be settled, signed on the line, and sealed, regardless of your circumstances, thoughts, and feelings.
God, through the blood of Jesus, makes an offer to you: the gift of salvation, that you don't have to earn or deserve, in exchange for your life. Repent of your sins and give your life to him in trust and love, and he will give the gift of salvation to you, signed, settled, and sealed. A simple done deal.
But is it so simple? What if you stray? What if you have all these doubts? What if you sin? What if your mind has all these wandering thoughts? What if your emotions are churning with things you hear, feel, think, and experience? In that case, return to rule #1: Your salvation is a matter of status and not of anything else. If you have given your life to Jesus in trust and love, if you have repented of your sins, then the free gift of salvation is yours. God will then begin the process of transforming your mind, healing your soul, training your emotions, settling your doubts, and loving away your fears. It's anything but a straight path, but is instead filled with obstacles, setbacks, successes, problems, joys, worries and doubts, and growth. Not to worry: if you are in God's hand he will not let you go. He will work with you to see you through it all. In His hand, he will work all things toward the goal of the good, and to your ultimately growth and salvation. As John 15 & Phil. 1.6 say, abide in him, and he will bring to completion the work he has begun in you.
Sorry I didn't listen to John Piper's sermon. He's a good speaker and a godly man; I just don't have an hour for that right now. If you have given your life to Jesus in trust and love, and if you have repented of your sins, then your salvation is genuine. The fears battling in you are both normal (common) and threatening. Go online and read the words to the hymn, "A Mighty Fortress Is Our God" (
http://www.hymnsite.com/lyrics/umh110.sht). I know it's "old-speak," but you should be able to discern it's meaning, truth, and power.
> How am I supposed to worship God if I can't be thankful for my salvation and his gifts?
Did your mom ever make you say thank you, when you were a little kid, even when you weren't particularly thankful? Some people say that actions must precede feelings, and in some things, that's true. We can be thankful to God even when we aren't feeling it, just like I still love my wife when we're having a, um, disagreement (fight). God saved you, say thank you. Worship him for what he's done, not for how you feel.
Talk to me some more. I know this is a big and complex subject, but mostly one that knots up our stomachs. I have an assignment for you. First read Psalm 86. Then in your prayers today just take deep breaths, spend a few minutes relaxing, and then fill your head with the grandest thoughts of God you can muster. Continue to breathe deeply, and rehearse the good things you know about him from the Bible. Breathe slowly and let Him fill your being. At the end say thank you and amen. Try it. Just let God be with you as you rehearse what you know, not what you feel right now (time for that will come later).