This is one of the most commonly asked questions and deserves an honest answer.  Below is first a short answer then a more thorough answer. There are three things we need to consider when answering the starlight question:

1.  Scientists cannot measure distances beyond 100 light years accurately. 

2.  No one knows what light is or that it always travels the same speed throughout all time, space and matter.

3.  The creation was finished or mature when God made it. Adam was full-grown, the trees had fruit on them, the starlight was visible, etc.

Let me elaborate on these 3 points. 

First, no one can measure star distance accurately. The farthest accurate distance man can measure is 20 light years (some textbooks say up to 100), not several billion light years. Man measures star distances using parallax trigonometry. By choosing two measurable observation points and making an imaginary triangle to a third point, and using simple trigonometry, man calculates the distance to the third point. The most distant observation points available are the positions of the earth in solar orbit six months apart, say June and December. This would be a base for our imaginary triangle of 186,000,000 miles or 16 light minutes. There are 525,948 minutes in a year. Even if the nearest star were only one light year away (and it isn’t), the angle at the third point measures .017 degrees. In simpler terms, a triangle like this would be the same angle two surveyors would see if they were standing sixteen inches apart and focusing on a third point 8.24 miles away. If they stayed 16 inches apart and focused on a dot 824 miles away, they would have the same angle as an astronomer measuring a point 100 light years away. A point 5 million years away is impossible to figure with trigonometry. The stars may be that far away but modern man has no way of measuring those great distances. No one can state definitively the distance to the stars. The stars may indeed be billions of light years away, but man cannot measure those distances.

Several other methods such as luminosity and red shift are employed to try to guess at greater distances but all such methods have serious problems and assumptions involved. For a more complex and slightly different answer to the star light question from a Christian perspective, see the book Starlight and Time by Russell Humphry available from www.icr.org.

Second, the speed of light may not be a constant. It does vary in different media (hence the rainbow effect of light going through a prism) and may vary in different places in space. The entire idea behind the black hole theory is that light can be attracted by gravity and be unable to escape the great pull of these imaginary black holes. No one knows what light is let alone that its velocity has been the same all through time and space. Since atomic clocks use the wavelength of the Cesium 133 atom as a standard of time, if the speed of light is decaying, the clock would be changing at the same rate and therefore not be noticed.

On February 18, 1999, Houston Chronicle ran an article on page 10A about a Danish Physicist, Dr. Hau working at Harvard, being able to slow down light by cooling it. They cool it to fifty-billionths of a degree above absolute zero -459.67. The light was slowed down to 38 MPH! 

In Dallas Morning News on 2-28-2000 the article says they have now slowed it to 1 MPH! See also New Scientist, July 24, 1999 pp. 28-32 and Science News, June 9, 1984, p.359 for more on gravity effecting light. 

"Eureka! Scientists break speed of light", Jonathan Leake, Science Editor, Sunday Times [UK] June 4, 2000. 
UNITED STATES SCIENTISTS claim they have broken the ultimate speed barrier: the speed of light. In research carried out in the United States, particle physicists have shown that light pulses can be accelerated to up to 300 times their normal velocity of 186,000 miles per second.  The work was carried out by Dr Lijun Wang, of the NEC research institute in Princeton, who transmitted a pulse of light towards a chamber filled with  specially treated cesium gas. See also: New York Times May, 30, 2000 www.nytimes.com 

Researchers say they have slowed light to a dead stop, stored it and then released it as if it were an ordinary material particle.  The achievement is a landmark feat that, by reining in nature's swiftest and most ethereal form of energy for the first time, could help realize what are now theoretical concepts for vastly increasing the speed of computers and the security of communications.  Two independent teams of physicists have achieved the result, one led by Dr. Lene Vestergaard Hau of Harvard University and the Rowland Institute for Science in Cambridge, Mass., and the other by Dr. Ronald L. Walsworth and Dr. Mikhail D. Lukin of the Harvard-Smithsonian Center for Astrophysics, also in Cambridge. 

During the last 300 years, at least 164 separate measurements of the speed of light have been published. Sixteen different measurement techniques were used.  "THE SPEED OF LIGHT HAS APPARENTLY DECREASED SO RAPIDLY THAT EXPERMENTAL ERROR CANNOT EXPLAIN IT!"
Astronomer Barry Setterfield
The Atomic Constants, Light, and Time 1987 

 "NO PHYSICAL LAW PREVENTS ANYTHING FROM EXCEEDING THE SPEED OF LIGHT. IN TWO PUBLISHED EXPERIMENTS, THE SPEED OF LIGHT WAS APPARENTLY EXCEEDED BY AS MUCH AS A FACTOR OF 100!" 

1."Thirty Six Nanoseconds Faster Than Light" Electronics and Wireless World 1988 pp 1162-1165 
2."Faster Than Light?" Radio-Electronics pp 55-58. 
    Also - New Scientist April 1, 1995; pp 26-29 "Faster Than What"
            Newsweek June 19, 1995 p 67-69

"The speed of light was ten billion times faster at time zero!"  -Dr. V.S. Troitskii, Cosmologist at the Radio-physical Research Institute in Gorky. "Physical Constants and the Evolution of the Universe" Astrophysics and Space Science, Vol. 139, No. 2, December 1987 pp 389-411. 

"A shocking possibility is that the speed of light might change in time during the life of the universe."  Dr. Joao Magueijo of Imperial College London www.Sunday-times.co.uk  12-24-2000 

The atomic clock. In 1956, following several years of work, two astronomers at the U.S. Naval Observatory (USNO) and two astronomers at the National Physical Laboratory (Teddington, England) determined the relationship between the frequency of the Cesium atom (the standard of time) and the rotation of the Earth at a particular epoch.  As a result, they defined the second of atomic time as the length of time required for 9 192 631 770 cycles of the Cesium atom at zero magnetic field. The second thus defined was equivalent to the second defined by the fraction 1 / 31 556 925.9747 of the year 1900. 

Third, the creation account states that God made light before He made the sun, moon, or stars. The rest of creation was mature, so starlight was probably mature at creation as well. I would ask the question, How old was Adam when God made him? Obviously he was zero years old. But how old did he look? He was a full-grown man. The trees were full-grown with fruit on them the first day they were made. The creation had to be that way; it would not work otherwise. Stars and their light were made at the same time. The God that I worship is not limited by anything involving time, space or matter.

Finally, I would also like to point out that the evolutionists have no answer to the basic questions like: Where did the original matter space and energy come from for the stars?  I suspect God built the universe so we would say "Wow!" When we see the stars we should be reminded of the glory of God not evolution. See Psalms 8.