Imagine that you're explaining God to a person who thinks He is merely an impersonal force. How would you defend the idea that God is personal (a) from the Bible and (b) from your experience?
I am so glad you have come to me with this. It makes for some good brain bending discussion.
By saying "impersonal", I assume that you mean that you think God is nothing more than some cosmic being in the universe. God is not "the force" of Starwars or just an "inner light". God is a person, He has a character and nature. He is knowable and desires to be known.
Biblically speaking there are innumerable passages where God speak to His people. If you want to get technical you can say that is what the Bible is- God's message to His people- and you would be correct. There is a literary tool that the writers of the Scripture employed frequently to communicate the nature of God. It is called anthropomorphism which uses human characteristics to describe non-human things. For example we know that God does not have a body, He is spirit, but the Psalmist speaks of His "mighty arm" in Psalms 89. This descriptor tell us that God is powerful. Passages like Deuteronomy 7:8 and Amos 5:21 describe how God feels and what His thoughts are about situations. Other places in Scripture like Malachi 3:6 explicitly tell us things about God's character and nature. God desires that we know Him. He has given us the Bible! A cosmic force would do no such thing. He uses language- human words- to communicate to us that He exists and who He is!
Experientially one of the best examples I have for the personal nature of God is conviction of sin, repentance, and forgiveness. When God convicts me of sin, there is an overwhelming experience in my heart that tells me I have offended a holy and just God. I have rebelled and need to do something about it. God clearly communicates that I must repent. In godly repentance there is true sorry for sin and a desire for reconciliation. My heart knows that God is calling me to come back to Him. I know that a "bruised reed He will not break". He will restore me. Having brought my sin before the LORD, I experience great joy and thankfulness at the forgiveness received. This reality is a ministry of the Holy Spirit. He works to bring to life the truth of the Word in my heart. I know that God cares that I be holy as He is holy. I know that He will bring me back to right standing. I know that there is joy in His presence. All of these are personal.
God reveals His personal nature through His Word and experientially through the minisitry of the Holy Spirit. This is definitely an incomplete discourse but hopefully enough to get you started.
I hope this was helpful to you!