When I put a voltmeter across those terminals, I measure "24V".
I wouldn't want that on an Arduino pin (or that of any "logic-level" device.) 
I believe that's indicative of an input pulled-up to 24V. 
What's the situation with yours?

What's a "doorbell opener"?

My garage door opener has two screw terminals, they get connected to the normally-open switch that's mounted next to the door.  If I short them with a screw-driver it's just like the switch does, and if I connect the contacts of a relay to them, same thing.  So, that's "why a relay".

You have not been degraded.
You are making a claim which is not supported by fact.
And nobody is a bad person for disagreeing with you.
I hope you will have as much character as you have chutzpah once you start drawing current from this "circuit" of which you are so incredibly enamored ("yours" or not) and faithfully report the results.

I posted a circuit awhile back and a number of people said it would never work.  Well because so many implied that I was crazy or worse I went ahead and built the circuit.
There seems to be a number of people that want to insult and degrade people.  So for those just ignore them.  If someone wants to help you, or you want to help, those are the people you need to associate with.  Remember you can always build the circuit and see for yourself.

It would have been nice if you had simply updated your subject
http://arduino.cc/forum/index.php/topic,103413.0.html

You are emotionally over-invested in your "design".
Start drawing some current from that, from both "outputs" -- at the same time.

...but I don't really grok the transistor yet.... it seems like my brain isn't as agile or adept as it was back in the 80's, when first studied electronics. One thing I was wondering, just the other day, was if there's a wall chart... I'm not sure exactly sure what I'd expect to find, but I figure there are some basic rules and characteristics which could be expressed.
(But I'm really visually oriented, so a poster would be really cool.)

After 30 years, man, it's like... well, hope springs eternal.
So, here's a "poster" (Take this, may it serve you well) ─

Final question, when I install this in m car, can I swap out the 9v battery with a connection to my car battery? (12v)

Yes.

... as in "via con Dios" - thanks again everyone.

Sorry, Norm-F, but that's "Vaya con Dios".  (:

* * * *
If you don't believe me, ask Freddy:
Sing along if you know the words!

10K for the base resistor?  If so, then use that 330Ω instead.

Too right.  That's one of the first words we got in class, via (puer, vir, agricola) Via Appia
Our teacher had us pronounce the Latin V as the English W (wee-ah ahp-pee-ah). 
Our books had U and V, even though the Romans only had V, and we didn't have to use the diacritical marks on the vowels (she told us that we were getting off easy.)

I dug out my Regenerative hybrid.
It has a varactor diode (MVAM109) for tuning, I used a voltmeter as a tuning dial.
It uses an NPN transistor for the regeneration.
I'll have to hunt around for the circuit.
There's a LM386 power amp, too, just for kicks.



www.photobucket.com/regen-hyb

http://en.wikipedia.org/wiki/Regenerative_circuit

* * * I found that schematic.  I tucked it inside one of my books.  It's with the other pics in the 'photobucket' link above. * * *

You can't just jump to FM like that.
Well, at least add regeneration, get some selectivity.

He probably means like "common emitter", but your way is OK, too.
In fact, your way, "common collector", the FET is On when the Arduino output is HIGH.

so in the lc circuit i can either keep a variable cap or a variable inductor?

Yes!
Most car radios used to use a variable inductor, less subject to drift vs. temperature compared to a variable capacitor.

I am familiar with this diagram:
But I can't seem to quite figure it out...

What's the trouble?

[I thought you were getting some relay board for this deal.]  http://arduino.cc/forum/index.php/topic,103055.0.html

Maybe there is room enough inside to place a photocell (a/k/a LDR).  There might be enough light from the LED to make for a reading from it, enough to tell if it's definitely light from the LED vs. ambient coming in through the LED's lens.  This way you'd leave the device electronics out of circuit.