American Airlines Virtual

Test your MIC volume control , too low VOL could be your problem.
Does the VVL info bar orange color bright when you pust to talk button is pressed?

Logging on to an airport and listen is good, I did it for hours when learning.
Now here is probably what is happening with your FSINN. There are about three places to set up the voice part of your system.
Make sure you computer is using your MIC. Right click your sound Icon at the bottom or go to the sound, recording part of your system setup on the control panel. Microphone properties, as sometimes the Mic option is turned off.
On your copilot setting for your FSINN on your FS menu page names settings, this is your addon management for FSFDT . look and you will see a page that lets you program keyboard strokes to FSINN. You need to make sure you INN VATSIM voice is programed tO your PTT button or keyboard button.
On the FSFDT Xmas tree on the bottom of your screen when you start VATSIM where the green lights are, right mouse click on that to open it up and there will be a list that says; config, voice, key management. Open the voice and there will be a box that says for FSS PTT joystick button or keyboard . You need to set what key your using.

These are the three places to set your computer. Make sure your mic is plugged in the correct hole. It is turned on if there is a MIc off button and you dial in the correct frequency to listen and talk.
That is it the rest is up to you. Vatsim does work with FSINN it is always the computer settings and the user.
Good Luck

Oscar -

FSX or FS9? If FSX, are you running FSInn as administrator?

Has FSInn ever worked (i.e. using same mic to speak to anyone)?