Think about what Jesus himself said, if your child asks you for an egg, which of you - though evil - will give him a serpent. How much more so will your Father in Heaven give to those asking him good gifts and perfect presents.
Accepting the Gift from God, Christ Jesus, will only ever bring you good things.
I'm realising that the first step a person needs to take to recognise the need for Jesus is for them to fully acknowledge that they're a sinner. How many JWs think of themselves as sinners? To them sinners are adulterers and murderers. I don't think many JWs genuinely feel like they actually need Christ's sacrifice to forgive their sins and that because of those sins they're totally cut off from God. I mean, when they go to the memorial, they obviously believe they do not need the means to forgive sins, hence they pass them on.
The Holy Spirit convicts us of our sins. It's when we feel the Holy Spirit from God pouring into our hearts that we feel the crushing weight of the debt of our sins, how we're completely unworthy of ever standing before God. But just as quickly, the Spirit baptises us and raises us from our dead condition and give us a new Spirit that places us in a position where we're no longer condemned (Rom 8:1) and in that moment we're born again, we're given a new life before God, a life where our sins are made white by the blood of the Lamb.
If you look at a piece of red clothing through a red filter, the clothing appears white. That's how our sin-stained lives are before God when we're in a relationship with Christ Jesus. He knew no sin, but he was made to become sin in order that we can be the righteousness of God. Receiving the Spirit of Christ (remember, the Holy Spirit is sent by the Father in Christ's name) means that we never again need to fear anything - Rom 8:15 "You did not receive a spirit that makes you a slave again to fear, but you received the Spirit of sonship. And by him (the Spirit of Christ) we cry, "Abba, Father"." 1 John 4:4 tells us that he who is in us is greater than he who is in the world. The Holy Spirit lives within us, we become the temple within which he dwells, and he daily works in us to create a new heart, new desires, new ways of thinking.
I definitely think you should "court" Jesus. I'd recommend reading Romans. If you can't stomach reading the whole letter, read just the 8th chapter. Verses 38 and 39 may help you.
I also think praying to God about your concerns and doubts is useful. Explain to him in simple terms that you've been abused and battered and you're afraid of not matching up or of letting him down.
Also, if you get the chance, John 9 is a great example of how Christ works, particularly when you get to verse 35.
If you want to chat about this stuff further, PM me and I'll give you my email address.