Hi Star -
you got the scripture right that people use for the "rapture" teaching but I don't believe you can spiritualize this verse. In other words say this means "spiritually dead". The reason being when Paul made the statement he said "we" who are still alive. in this "we" he includes himself and therefore means believers. He was saying those (believers) who die would not recieve their reward (heavenly nature) ahead of them but rather when Christ comes again, those believers in the graves will be raised and at the same time - "we" believers alive on earth will be taken up too. That is when the corruptable puts on the incoruptable meaning we have a change of nature to the heavenly one. And we will be able to be with the Lord in the heavenly realm. Only believers recieve this change of nature. Read all of that verse in corinthians. This is what the "rapture" comes from although this word is not in the bible. What do "we" do in heaven - reign with Christ for 1,000 years.
I noticed you quoted the other text Daniel 12 that speaks about the same thing. Matthew 24 also mentions taking up believers to go to heaven. One thing though it is not uncommon for events in the bible to be included in one paragraph yet, they take place in different time periods. Although Daniel shows two types of people being raised, believers and non-believers, most bible scholars agree that in light of other scriptures these events take place at different times. One scripture used to support this view is Revelation 20:4,5
The rest of the dead - (unbelievers) do not come alive until the 1,000 years has ended. See Revelation 20:4,5.
Just a note: the WT teaches if "we" reign we must reign over others on the earth and thus there are two classes of Christians. The reigning with Christ in Revelation clearly shows reigning in heaven not over the earth as the other dead are not alive at that time. In other words, there are no subjects on earth to reign over.
There are many theories about what happens to those left on earth. Too complicated to get into at this time. As far as when this will happen, being taken to heaven that is - Jesus said "no one knows the date and hour but only the father in heaven knows" and admonished us to stay awake not to be concerned with a date and time. Christians even in Jesus day lived in expectation that it could occur at any time but as someone else already pointed out, it could be many years away. We just do not know. Lilly