In your study on Cornelius, you indicated that receiving the Holy Spirit did not necessarily indicate that a person believed or was saved. You cited the examples of Saul and Balaam as proof, but doesn't Acts 5:32 contradicts this?
The study being referred to is "Cornelius Received the Holy Spirit". Acts 5:32 states, "And we are His witnesses to these things, and so also is the Holy Spirit whom God has given to those who obey Him."
First, please notice that Peter's statement is not exclusive. Peter did not state that the Holy Spirit is only given to those who obey God. If it was exclusive then there would have been a contradiction between Peter's statement and the events that occurred to King Saul in I Samuel 19:18-24 and to Balaam in Numbers 23:1-5 and II Peter 2:15. Neither Saul nor Balaam were righteous men, yet the Spirit was given to them for a specific purpose.
Second, notice that the Spirit is given by God to those who obey Him. In particular, I would like to you note that belief is not mentioned. This is in agreement with what Peter stated earlier, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call" (Acts 2:38-39). Peter stated that the gift of the Spirit would be given to those who repent and are baptized. Such is consistent with Acts 5:32. Yet, while belief is not specifically mentioned, it is implied, and it is shown in Ephesians 1:13-14, "In Him you also trusted, after you heard the word of truth, the gospel of your salvation; in whom also, having believed, you were sealed with the Holy Spirit of promise, who is the guarantee of our inheritance until the redemption of the purchased possession, to the praise of His glory." Paul's statement in Ephesians is not contradictory to Peter's two statements in Acts. Instead, it is additive -- it gives us further details -- because none of the statements are exclusive.
Hence, the Spirit is given to all who have been saved, the conditions of which are faith, repentance, and baptism. Yet, the Bible does not state that the Spirit cannot be given to the unfaithful. Instead, the Bible records a few occasions where the Spirit was given to the disobedient to make a point. In the case of Cornelius, the point was not to show that Cornelius was saved, but to show that Gentiles were acceptable to God while remaining Gentiles. Quoting from the original article:
So why did the Spirit come upon Cornelius and his household? The answer is clearly stated by Peter in Acts 15:8-11. "Men and brethren, you know that a good while ago God chose among us, that by my mouth the Gentiles should hear the word of the gospel and believe. So God, who knows the heart, acknowledged them by giving them the Holy Spirit, just as He did to us, and made no distinction between us and them, purifying their hearts by faith. Now therefore, why do you test God by putting a yoke on the neck of the disciples which neither our fathers nor we were able to bear? But we believe that through the grace of the Lord Jesus Christ we shall be saved in the same manner as they." God acknowledged them, or bore them witness, or testified to them (depending on your translation) by giving them the Holy Spirit.
Hence, our next question ought to be, "A witness to what?" Some time after Cornelius's conversion the issue was raised as to whether a Gentile had to become a Jew before he could be saved. "Some of the sect of the Pharisees who believed rose up, saying, "It is necessary to circumcise them, and to command them to keep the law of Moses" (Acts 15:5). Peter's response to this was to point out that the Spirit came to witness that these Gentiles could be saved without being first a Jew. But take note that Peter did not say that the Spirit came to witness that a person could be saved without baptism.
This then leads to the question, "Why did the Spirit come before Cornelius was baptized in water?" In order to answer this question, you need to notice that six Jewish Christians had accompanied Peter to Cornelius's house (Acts 10:23; 11:12). As stated in the text, the Spirit's coming was a shock to these men. "And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also. For they heard them speak with tongues and magnify God" (Acts 10:45-46). Peter then turned to these same men and asked if they dare object to Cornelius being baptized in water given the obvious testimony of God (Acts 10:47; 11:17).
Also, notice that the Spirit did not come upon the Gentiles until Peter began to speak (Acts 11:15). Here was testimony to all that Gentiles could be saved through the word of God (Acts 11:13-14).
When Peter testified at the gathering in Jerusalem, recorded in Acts 15, he used the example of Cornelius to prove that Gentiles, while remaining Gentiles and not becoming Jews, were accepted by God. Peter did not use the case of Cornelius to prove that everyone should receive the Spirit, or that the Spirit burnt sin out of a sinner's heart, or that the Spirit's coming made him a child of God. Instead, we find that Peter used the baptism of the Spirit as proof that Cornelius and his household should be baptized in water, as recorded in Acts 10 and Acts 11. Peter consistently argued that the Gentiles were to receive the gospel without being bound to the Law. For anyone to claim otherwise would be trying God. "Now therefore, why do you test God by putting a yoke on the neck of the disciples which neither our fathers nor we were able to bear?" (Acts 15:10).