INSTRUCTOR WITH STUDENT TAXI PAST VERY WORN HOLD LINE.

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STUDENT AND I CALLED LUK GND AFTER RECEIVING THE ATIS AND WERE INSTRUCTED TO TAXI TO RWY 3R. MANY ADDITIONAL ACFT WERE ALSO ARRIVING/DEPARTING RWY 3R AND THE CTLR'S WORKLOAD WAS VERY HIGH. AS OUR FLT PROCEEDED DOWN TXWY C TOWARD RWY 3R; WE VOLUNTEERED TO HOLD FOR A CHALLENGER TO PULL OUT OF FBO AND TAXI AHEAD OF US TO RWY 3R. FOLLOWING THE CHALLENGER AND TRYING TO MAINTAIN SITUATIONAL AWARENESS WITH THE ACFT AROUND US; WE CONTINUED ALONG TXWY C WHILE SEARCHING FOR THE STANDARD YELLOW HOLD SHORT LINES. AS WE SLOWLY ROLLED ONWARD TOWARD THE THRESHOLD OF RWY 3R; IT BECAME APPARENT THAT WE MUST HAVE MISSED THEM. SO WE STOPPED IMMEDIATELY; STILL WELL CLR OF ANY OPS ON RWY 3R; AND LOOKED BEHIND US. SURE ENOUGH; THE REMNANTS OF THE VERY HEAVILY WORN AND FADED HOLD SHORT LINES COULD JUST BARELY BE SEEN ALONG THE EDGES OF THE TXWY AND WERE ALMOST INVISIBLE ON THE REMAINING WIDTH OF THE TXWY. OUR ACFT HAD ROLLED APPROX 15 FT PAST THE LINE BUT WAS STILL AT LEAST 30 FT FROM THE L (OR CLOSEST) EDGE OF THE RWY. THE RWY ITSELF WAS 150 FT WIDE. WE WERE SHORTLY THEREAFTER CLRED FOR TKOF WITHOUT FURTHER INCIDENT. EVEN THOUGH THE HOLD SHORT LINES WERE VERY WORN/FADED; WE SHOULD STILL HAVE BEEN ABLE TO IDENT THE HOLDING POINT USING THE RED/WHITE TXWY/RWY INTXN MARKERS. WHILE WE WERE BOTH CONCENTRATING TO SEE THE HOLD SHORT LINES; I HONESTLY DO NOT REMEMBER SEEING THE RED/WHITE INTXN MARKERS. IN THE FUTURE; I WILL BE MORE ALERT TO MULTIPLE MEANS OF IDENTING A PARTICULAR SPOT; RTE; ETC; AND NOT ALLOW ATTN TO BECOME OVERLY FOCUSED/LIMITED ON 1 ITEM; NO MATTER HOW BUSY THE WORKLOAD. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES HE HAS HAD NO FOLLOW-UP ON THIS INCIDENT. HE WAS QUITE SHOCKED TO LOOK BACK AND SEE THESE 'PIECES' OF YELLOW LINES FROM THE EDGE OF THE TXWY THAT FADED INTO NOTHING ON THE CTR TXWY AREA. HIS REF TO RED/WHITE MARKINGS IS REFERRING TO THE RWY SIGNS ONE WOULD SEE BESIDE THE TXWY INDICATING THE RWY AHEAD. HE HAS LEARNED; AS HAS HIS STUDENT; TO MONITOR MORE THAN 1 INDICATOR.