The reason you see no connection between the age of the Earth and the time it takes light to travel from stars within our own galaxy to Earth is because there is none: I said nothing about our planet but was talking about the age of the Universe.
Then you have really bad reading comprehension skills because you commented on my comment about how old the world is.
No one knows how old the universe OR the world is. Period.
Good thing scientists don't simply take your word for it.
These scientist throw out results that don't fit what they believe to be correct and keep the ones that do.
"The troubles of the radiocarbon dating method are undeniably deep and serious ... It should be no surprise, then, that fully half of the dates are rejected. The wonder is, surely, that the remaining half come to be accepted." (Lee, R. E., Radiocarbon, "Ages in Error", Anthropological Journal of Canada, 1981, vol. 19, No. 3, p. 9) (Ham, Snelling, & Wieland)
There are also some tests that have been done that dont quite match up. For instance, bones of a sabre-toothed tiger, theorized to be between 100,000 and one million years old, gave a Carbon date of 28,000 years. A freshly killed seal, dated using Carbon-14, showed it had died 1300 years ago. Living mollusk shells were dated at up to 2,300 years old. Some very unusual evidence is that living snails' shells showed that they had died 27,000 years ago. (Ham, Snelling, & Wieland)
Sources:
Chemistry: Molecules, Matter, and Change
By Loretta Jones and Peter Atkins
W.H. Freeman and Company, New York, 2000
Carbon-14
By Lynn Poole
Whittlesey House, 1961
The Carbon-14 Dating of Iron
By Nikolaas J. Van Der Merwe
The University of Chicago Press, Chicago, 1969