If it boots, the battery damage hasn't killed it. Remove the battery, clean the MB and it should be good to go for a long time. Hard to tell how bad it is from the listing photo. It looks Ok to me, no green stuff on the MB which is the state my A4000 came in. I just cleaned it up after removing the battery and no further damage was done and it's been working for me since 2007.
In the A2320 card there is a tweak pot that sometimes needs to be adjusted. Might be similar on the A3000. I've never owned one and I'm not familiar with the fine details of the hardware.