Chosen Solution
The smell started 2 weeks before it died but it worked fine until an hour before it died. Then the signal decreased to the point that the internet slowed to unusable, but my iPhone had a great signal right up to the demise. Is this repairable?
We had a similar issue around the office, which we talk about how to fix here. They talk about it in the article, but it bears repeating here: This is not an official iFixit Guide, do not expect prefect results if you attempt it. We published it more as a hack-fix interest piece.
To answer that question you need disassemble your Airport Express and look after burned parts on the Logic Board and exchange them. If there are no burned parts on the Logic board the broken part presumably is the power supply which can be changed fast&easily.
First sorry for my bad english :-) If the airport is power on but after a while the LED turn off then look for the capacitor on the power bord. If the fuse i blown then look for the diode is shorted. The LED will be off all time then If the fuse is blown and its not the diode then change the hold power supply. If the capacitor is leaking or is not flad on the top change those or test it whit a capacitor tester that the capacitor has is µF BEST REGARD FROM DENMARK
The fuse is blown and the diode is shorted. And your English is quite good.