No, God hasn't given up on you. If He had, you wouldn't feel guilty or even be asking me this question. God is working in your heart, convicting you of your sins and drawing you back to Himself. Would He be doing this if He weren't willing to forgive you?
The key is to look not only at how bad you are, but at how good Christ is. Elsewhere, you mention that you grew up in a church and were active there as a youth. You know, therefore, who Jesus was: the sinless Son of God, sent from heaven to save us from our sins. He did this by becoming the final and complete sacrifice for our sins through His death on the cross. The Bible says, "He appeared so that he might take away our sins" (1 John 3:5).
Did Jesus die for you? Does Jesus want you to be part of His family and be with Him in heaven? Certainly! Turn to Him today, confessing your sins and asking Him to forgive you and come into your life. The Bible says, "In him we have redemption through his blood, the forgiveness of sins" (Ephesians 1:7).
Then ask God to help you resist temptation and live for Christ every day. Ask Him also to lead you to other believers (perhaps in your post's chapel) who can help you.