Actually, a modem CAN detect a pick-up...
or should I say, it can detect the ring tone, and then detect when the ring tone stopped...

So, to detect the pickup...
Call the person
modem will return a "<DLE>r" (not sure if r really stands for ring, but I'm assuming it is)
so for every ring you get (say it rings 3 times before the person picks up)
<DLE>r
pause 0.5 seconds
<DLE>r
pause 0.5 seconds
<DLE>r
pause 0.5 seconds
wait another ... say 0.1 seconds, if there is no more <DLE>r, then the phone was picked up, so start playing the message

When calling you can have a few outcomes, it rings, no one picks up, or picks up, then hangs up right away, there is a <DLE> for that too, or also, you can get a busy tone, and of course there is a <DLE> for that too....

To play the wave
First of all you need a voice modem, most computers don't come with a voice modem because not many people are actually using that feature, so you probably have to buy one.

Then you have to initialze the sound on the modem (using the comm control), choose the same format as the wave file (message you want to play), (or convert the wave file to the format that the modem can play), and finally, stream the wave file on the comm port.

See this thread on how to initialize the sound on the modem:
http://www.vbforums.com/showthread.php?t=365345 (look at my posts)