Way back my A3000 died in a very simular way. I spent like $300 (ripped off) to have it repaird and it died again a month later. I left it for dead. Five years later I revisited it only to find the problem to be the daughter card wasn't seated perfectly.
If it's not seated perfectly or the connetions are a little dirty then it won't boot.
I'm not sure if the A3000T has this problem or not though...