Isn't the "gift" the Holy Spirit? Reading the scriptures, the Holy Spirit only comes upon one after baptism and the laying on of hands:
Act 8:15 who when they had come down, prayed for them that they might receive the Holy Spirit.
Act 8:16 For as yet He had not fallen on any of them, they were baptized only in the name of the Lord Jesus.
Act 8:17 Then they laid their hands on them, and they received the Holy Spirit.
Act 8:18 And when Simon saw that the Holy Spirit was given through laying on of the apostles' hands, he offered them money,
Or:
Act 19:5 And hearing, they were baptized in the name of the Lord Jesus.
Act 19:6 And as Paul laid his hands on them, the Holy Spirit came on them, and they spoke with tongues and prophesied.
With that in mind, then:
1 Tim 4:14 Do not neglect the gift in you, which was given you by prophecy, with the laying on of the hands of the body of elders.
This verse only seems to mean that the Holy spirit was given to Timothy and that he was to stir it up, not neglect it, as everyone who receives it should.
That is one interpretation. I don't agree with it. I believe that the laying on of hands that Paul is talking to Timothy about was his ordination. I believe that the laying on of hands in Acts is a description of what we now call Confirmation, which is the sacrament in which a baptized person who had been properly instructed in the Faith, receives the seven fold gifts of the Holy Spirit.