The verse you quoted (LK 11:13) actually disputes what you are trying to teach:
Lk 11:13 If ye then, being evil, know how to give good gifts unto your children: how much more shall [your] heavenly Father give the Holy Spirit to them that ask him?
It clearly states that those to whom he was speaking were evil.Yet God in his mercy would still give them the empowerment they needed to overcome. To overcome sin one must walk in the Spirit. This cannot be done without the Holy Spirit.
You also pull John 9:13 out of context and misapply it. The whole concept of "God not hearing sinners" was an understanding based on being under the Mosaic law.
After the sacrifice of Christ we are all made clean by his blood. God does not refuse the cry of the broken and humble. If your extrapolation were true then God would not have heard David in Ps 51 when he cried,after committing adultery and murder, for God to not take his Spirit from him.
Clear proof that David had the Spirit the entire time he was caught up in his sin. If "God doesn't hear sinners" then no sinner can ever be forgiven.
I apologize to you,Kingsdaughter for this derail. Just couldn't let this lie slide by.