Can't communicate/access/find/etc Airport Express

Question

I have a spare Airport Express that I wanted to use to extend the wireless signal in our new house. I haven't used it in about a year, but it was working before I put it away as far as I remember.
When plugging it in, it briefly shows a green light, goes out, and then shows a steady yellow light. Once in a while it briefly turns to green then back to yellow immediately.
It does not put out any WiFi signal.
If I plug in an ethernet cable and try to run Airport Utility with it plugged into ethernet, my network settings say either "No IP Address" or that there is no device at the other end of my ethernet cable.
I have tried to reset it about 1000 times. While plugged in I hold down Reset for 10 seconds (light blinking yellow) and I have also tried unplugging it, holding down reset, then plugging it back in and holding it again.
Basically, I have no way of accessing it at all.
On any normal day I'd cut my losses and go buy a new one, but money is tight the next couple of months so I'd really like to get this thing working any way possible.

Answer 1

Thanks for the reply Bob!
I didn't have a hacksaw handy, but my wife did have a dremel with a cutting disc
Here was our adventure, delving into the internals of our Airport Express:
http://sphotos.ak.fbcdn.net/hphotos-ak-snc3/hs333.snc3/292481426068702953_1569863761_31018439_3281999n.jpg
And when all was said and done - here it is, good as new! Can't even tell it's ever been opened
http://sphotos.ak.fbcdn.net/hphotos-ak-ash1/hs342.ash1/292481426071863032_1569863761_31018448_4448936n.jpg
Works like a charm now!
(okay, okay, it's dead, but it was a lot of fun cutting it open! Perhaps the "unless you are really handy with small electronic repairs" should have been capitalized, and in bold LOL)