Paul defines the apostolic ministry and message in these terms:
For we do not proclaim ourselves; we proclaim Jesus Christ as Lord and ourselves as your slaves for Jesus' sake (2 Cor 4.5).
With this Paul sets up an essential link between evangelism and service: apostolic, evangelistic ministry is simultaneously the proclamation of the lordship of Jesus of Nazareth and the declaration of the apostles as the servants of others. The link is essential because Jesus as Lord himself was a servant. Paul elsewhere writes: Christ did not please himself (Rom 15.3). Rather, Christ himself defines his own ministry as service for the sake of the many, a service which involved his giving his own life for the sake of the life of the world (cf. Mark 10.45; John 6.51).
For this reason evangelism without service is dead and ineffective. This is one principal reason for which campus preachers do no good, like those at my alma mater Arizona State who hold up signs condemning "fornicators, masturbators, liars, cheaters," etc. to hell. Perhaps we may even dare to say that what they are doing is not evangelism at all. They don't serve anyone, they just make enemies for themselves and through their incompetent presentation of a false gospel they needlessly contribute to the hardening of so many undergraduate students.
True evangelism involves service; it involves offering yourself for the good of the persons whom you are evangelizing, showing goodwill and sincerity towards them. Apart from this, the persons listening to your message have no reason to believe you actually want good of them. You may just be one more religious person who wants me to come to your church so you can tell me what to believe and take my money from me. But if you put yourself at their disposal, if you are willing to care for them in a way that is meaningful for them, then you will have won them over. Christ himself won people over to his gospel through simultaneous proclamation and healing, providing, feeding, teaching, etc. The kingdom of heaven will be filled with masses of the formerly sick, blind, lame, paralytic, deformed whose bodies Christ healed and whose hearts simultaneously he won over.
At the same time, however, Paul does preach Jesus Christ as Lord, and not just himself as the slave of all. Service is one crucial element of evangelism, but so is the real, verbalized proclamation of Jesus Christ as Lord. Otherwise it is merely service and not evangelism. There's nothing wrong with mere service, of course. Sometimes it may do us good merely to serve, an exercise in unconditional love of the other person who may even reject our gospel message. But evangelism requires an euangelion, a good news that is unavoidably verbalized and communicated. And this euangelion is not about us or our goodwill, but about the goodwill of God towards us in Jesus Christ. That is why mere service cannot be evangelism: all it communicates to the other is our goodwill, which is not enough ultimately to save anyone.