Does baptism play a role in being born again?
Being born again is entirely a spiritual experience - it takes place when a person puts their faith in Jesus Christ (see the link: Spiritual Rebirth). Water baptism is only a ritual (whether we are talking about John's, Jesus', or believer water-baptism - not to be confused with the Spirit baptism all believers receive on faith in Christ: Rom.8:9). Water-baptism has nothing to do with salvation or eternal life. The important thing in rebirth is faith, for it is only through faith in Jesus Christ that a person receives God's new life (1Jn.5:10-12) and passes from death to life (1Jn.3:14; cf. Jn.5:24).
On the topic of being born again, please consult these links:
Spiritual Rebirth (in Peter #19)
A New Creature: Being Born Again
Born Again at Salvation
A Fresh Start for the Heart (in Peter #26)
Bible Basics 4B: Soteriology: the Biblical Subject of Salvation
Please see also the following links for more about the subject of baptism:
Baptism: Water and Spirit
Baptism and Following Jesus
Is Baptism Necessary for Salvation?
The 'baptism which now saves you': 1st Peter 3:21.
An Extended Conversation about the Baptism of the Holy Spirit.
Is water baptism required for Christians today?
Hope this helps,
Yours in Christ,