Well, I think I might've found the problem with the "new" A2000:
http://imgur.com/oIQQhtS
Yikes!
What's the best newbie-friendly way to clean this up? I'm not gonna be crushed if this mobo is dead forever, but if nothing else I'd like to practice my battery cleanup technique on this board before I attempt the same on my mostly-working Rev. 6.2 board...
Thats the CPU and at a minimum you need to pull it out and clean up those pins.
Go get yourself a big bottle of 99.9% of Iso NOT rubbing or store bought stuff, get 99.9 at least! You also need to get a bottle of concentrated lemon juice.
Brush on the lemon juice over the green areas and let it soak in good. Use an old tooth brush and scrub the effected areas off. Do it a few times if you need, its got to be done and it needs to get into all the problem leaking spots. you have a good chance of traces being damaged even more during this process, but you cant avoid it. Just do it.
Once it clean use the 99.9% Iso and scrub the entire board. Do be shy with it, clean everything. Scrub with the tooth brush (after you cleaned it out from the lemon juice) and be sure to get all the lemon out.
I like to use clean, non colored tissue paper. NOT the stuff you blow your nose with, the paper thats feels like the type you find in a public bathroom and goes over the seat. Take this and put it over the area you want clean. Take an acid brush and rub the Iso over that spot so the paper soaks up the crap under it. Use a clean piece for ever area until the board is dirt and contaminant free.
If you have canned air you can blow dry the board from iso in between cleanings too and again once complete.
Use a meter to find any open traces and a GOOD magnifier to find the once you cant see. They are there, trust me. Fix them with good solid core wire or a trace repair kit that uses copper foil and epoxy.
Its a long expensive process, but can be done.
Iso I use:
Lemon Juice: