Well, I had the nightmare happen today.
Got in the car this morning and had the dreaded "Click click click click" and no start. Did some searching and found this thread, and I am PRAYING that this is my solution. I got the RCM out today, unfortunately I don't have a solder gun. Going over a friend's house tomorrow to use his and hopefully fix it.
Meanwhile, borrowing my gf's Dodge Neon to get to work :|
Anyways, here is the RCM and the solders in question. I know it's blurry, but I don't really know exactly what I'm looking at. It doesn't appear to be corroded like the original poster's picture, but it has almost no solder on the top.
I'll let you all know tomorrow!! Crossing my fingers!!