Adding more informationI found a third fob that only functioned when it wanted, so I decided to do the same repair/de-corroding as described above. Except this time I took pictures.
1. Take the fob completely apart. You'll need a jewelers sized Phillips to remove the three small screws that hold in the circuit board.
Make absolutely sure that you remove the battery. If you use this de-corrosion method with a battery installed you will actually make corrosion, and could eat away and possibly destroy the smaller electrical conductors.
Of the three fobs I've de-corroded one had corrosion on the pins of both ICs on the back of the board.
Two of the fobs had corrosion inside of the push button switches on the front of the circuit board. The switches are the two identical square metal items mounted at a 45 degree angle with a round "button" in the center.
I used Lime Away as a readily available acid that is also fairly safe. Even so I made my acid solution by diluting it about 50/50 with warm tap water.
IMPORTANT: This is an acid!! Protect your eyes!! And avoid extended contact with your skin!!
Next I placed the circuit board in a small glass dish of the acid solution and watched for a reaction with the corrosion, which is a stream of fine bubbles. This board had no corrosion to speak of on the back, but the following picture shows the front with bubbles coming out of the push button switches and a bit of foamy froth floating on the top of the acid solution.
Because the acid is consumed by the corrosion as it is eliminated you have to agitate the solution every 5-10 minutes or so. This is to make sure there is fresh acid at the site of the corrosion. I used my index finger to shake the circuit board for about 5 seconds, with a quick tap water rinse after the agitation. (Rinse the finger, not the circuit board.)
I soak the circuit boards until the foaming stops, which was about 20 minutes for this particular circuit board.
After the acid I soak the board in warm tap water to wash out any remaining acid. I soak for at least 60 minutes and agitate every 10-15 minutes. (I don't use a base, like baking soda, to neutralize the acid because the base and acid reaction will form a salt. I'd rather use lots of water to flush the acid out and sidestep the whole issue of needing to wash out some kind of salt.)
Next step is drying. I used canned air to blow the obvious moisture away, followed by air drying for a couple of hours in a warm, dry place. If you don't have canned air then shake it off and leave it overnight in a warm dry spot.
When dry just put the thing back together. Cross your fingers and see if your fob works again.
Now an update from the next morning.... This fob now appears to work, although it hasn't stood the test of time like the first two did. (I waited approximately 2 months after the repair before I made my first post.)
thing I forgot to mention. In the cases of all three repaired fobs they did not work right away. I had to press the unlock more than 10 times before the fob worked unlocking the car. I suspect that if an Alpine fob hasn't been used in a while, even if it is programmed for the car, there may be some synchronization going on.