Q: Airport Extreme , no power light

Check to see if the outboard power supply "brick" will deliver a steady 12 volts. If it doesn't, then the issue may be the outboard power supply.  It might be a $20 risk to find out though, if the seller will not agree to issue a refund if you want to return the part.

http://www.ebay.com/itm/ORIGINAL-OEM-APPLE-AIRPORT-EXTREME-BASE-STATION-POWER-SU PPLY-AC-ADAPTER-A1202-/370810566512

If a new outboard power supply does not do the trick, then there is an internal power issue on the AirPort Extreme. Since Apple does not offer repair parts, and it would cost far more to rob another used AirPort for parts, the AirPort Extreme should be replaced.

You don't indicate which model number of AirPort Extreme that you have, but the average useful life of the AirPort is about 4-5 years.