the New American Standard (generally more reliable than KJV for various reasons) translates it thus:
" who, although He existed in the form of God, did not regard equality with God a thing to be grasped,"
for [face=SPIonic]uparxw[/face] Bauer lists two definitions:
1. exist (really) , be present, be at one’s disposal; be (found) somewhere; (with tini) what belongs to someone, someone’s property, possessions, means
2. as a widely used substitute in H.Gk. for ei\nai w. a predicate noun and oft. Very freq. in the ptc. w. a predicate noun who is, since he is, etc.
Note that neither of these indicate "beginning to be", but simply "being".
Since Bauer considers the first to be a common substitute for the second, I doubt that there is any exegetical significance.
Liddell lists more meanings for the word which include the one you gave... however, when it comes to specifically koine it's usually safest to trust Bauer, since Liddell goes all through classical greek and the word meanings changed so much...